diff --git a/lib/matplotlib/_constrained_layout.py b/lib/matplotlib/_constrained_layout.py
index 7ced20b3cf50..ec01448c524e 100644
--- a/lib/matplotlib/_constrained_layout.py
+++ b/lib/matplotlib/_constrained_layout.py
@@ -17,7 +17,7 @@
 
 import numpy as np
 
-import matplotlib.cbook as cbook
+from matplotlib import _api
 import matplotlib.transforms as mtransforms
 
 _log = logging.getLogger(__name__)
@@ -94,9 +94,9 @@ def do_constrained_layout(fig, renderer, h_pad, w_pad,
                 gss.add(gs)
     gss = list(gss)
     if len(gss) == 0:
-        cbook._warn_external('There are no gridspecs with layoutgrids. '
-                             'Possibly did not call parent GridSpec with the'
-                             ' "figure" keyword')
+        _api.warn_external('There are no gridspecs with layoutgrids. '
+                           'Possibly did not call parent GridSpec with the'
+                           ' "figure" keyword')
 
     for _ in range(2):
         # do the algorithm twice.  This has to be done because decorations
@@ -122,9 +122,9 @@ def do_constrained_layout(fig, renderer, h_pad, w_pad,
             _reposition_axes(fig, renderer, h_pad=h_pad, w_pad=w_pad,
                              hspace=hspace, wspace=wspace)
         else:
-            cbook._warn_external('constrained_layout not applied because '
-                                 'axes sizes collapsed to zero.  Try making '
-                                 'figure larger or axes decorations smaller.')
+            _api.warn_external('constrained_layout not applied because '
+                               'axes sizes collapsed to zero.  Try making '
+                               'figure larger or axes decorations smaller.')
         _reset_margins(fig)
 
 
diff --git a/lib/matplotlib/animation.py b/lib/matplotlib/animation.py
index 3bf6cc1b601f..16f509e98684 100644
--- a/lib/matplotlib/animation.py
+++ b/lib/matplotlib/animation.py
@@ -475,7 +475,7 @@ def frame_format(self, frame_format):
         if frame_format in self.supported_formats:
             self._frame_format = frame_format
         else:
-            cbook._warn_external(
+            _api.warn_external(
                 f"Ignoring file format {frame_format!r} which is not "
                 f"supported by {type(self).__name__}; using "
                 f"{self.supported_formats[0]} instead.")
diff --git a/lib/matplotlib/artist.py b/lib/matplotlib/artist.py
index a3929e36f042..0a238267b20d 100644
--- a/lib/matplotlib/artist.py
+++ b/lib/matplotlib/artist.py
@@ -901,8 +901,7 @@ def set_rasterized(self, rasterized):
         rasterized : bool
         """
         if rasterized and not hasattr(self.draw, "_supports_rasterization"):
-            cbook._warn_external(
-                "Rasterization of '%s' will be ignored" % self)
+            _api.warn_external(f"Rasterization of '{self}' will be ignored")
 
         self._rasterized = rasterized
 
diff --git a/lib/matplotlib/axes/_axes.py b/lib/matplotlib/axes/_axes.py
index 40c5a7dc95bc..40959b06fe64 100644
--- a/lib/matplotlib/axes/_axes.py
+++ b/lib/matplotlib/axes/_axes.py
@@ -4722,9 +4722,8 @@ def reduce_C_function(C: array) -> float
         # Set normalizer if bins is 'log'
         if bins == 'log':
             if norm is not None:
-                cbook._warn_external("Only one of 'bins' and 'norm' "
-                                     "arguments can be supplied, ignoring "
-                                     "bins={}".format(bins))
+                _api.warn_external("Only one of 'bins' and 'norm' arguments "
+                                   f"can be supplied, ignoring bins={bins}")
             else:
                 norm = mcolors.LogNorm()
             bins = None
@@ -5436,9 +5435,9 @@ def _pcolorargs(self, funcname, *args, shading='flat', **kwargs):
         try:
             _api.check_in_list(_valid_shading, shading=shading)
         except ValueError as err:
-            cbook._warn_external(f"shading value '{shading}' not in list of "
-                                 f"valid values {_valid_shading}. Setting "
-                                 "shading='auto'.")
+            _api.warn_external(f"shading value '{shading}' not in list of "
+                               f"valid values {_valid_shading}. Setting "
+                               "shading='auto'.")
             shading = 'auto'
 
         if len(args) == 1:
@@ -5523,7 +5522,7 @@ def _interp_grid(X):
                     if np.shape(X)[1] > 1:
                         dX = np.diff(X, axis=1)/2.
                         if not (np.all(dX >= 0) or np.all(dX <= 0)):
-                            cbook._warn_external(
+                            _api.warn_external(
                                 f"The input coordinates to {funcname} are "
                                 "interpreted as cell centers, but are not "
                                 "monotonically increasing or decreasing. "
diff --git a/lib/matplotlib/axes/_base.py b/lib/matplotlib/axes/_base.py
index b5e3fc7ac3cd..f2106fd00592 100644
--- a/lib/matplotlib/axes/_base.py
+++ b/lib/matplotlib/axes/_base.py
@@ -268,7 +268,7 @@ def __call__(self, *args, data=None, **kwargs):
                     label_namer_idx = 1
                 else:
                     if replaced[1] is not args[1]:  # case 2a)
-                        cbook._warn_external(
+                        _api.warn_external(
                             f"Second argument {args[1]!r} is ambiguous: could "
                             f"be a format string but is in 'data'; using as "
                             f"data.  If it was intended as data, set the "
@@ -2456,7 +2456,7 @@ def margins(self, *margins, x=None, y=None, tight=True):
 
         if x is None and y is None:
             if tight is not True:
-                cbook._warn_external(f'ignoring tight={tight!r} in get mode')
+                _api.warn_external(f'ignoring tight={tight!r} in get mode')
             return self._xmargin, self._ymargin
 
         if tight is not None:
@@ -3442,19 +3442,19 @@ def set_xlim(self, left=None, right=None, emit=True, auto=False,
             # so only grab the limits if we really need them.
             old_left, old_right = self.get_xlim()
             if left <= 0:
-                cbook._warn_external(
+                _api.warn_external(
                     'Attempted to set non-positive left xlim on a '
                     'log-scaled axis.\n'
                     'Invalid limit will be ignored.')
                 left = old_left
             if right <= 0:
-                cbook._warn_external(
+                _api.warn_external(
                     'Attempted to set non-positive right xlim on a '
                     'log-scaled axis.\n'
                     'Invalid limit will be ignored.')
                 right = old_right
         if left == right:
-            cbook._warn_external(
+            _api.warn_external(
                 f"Attempting to set identical left == right == {left} results "
                 f"in singular transformations; automatically expanding.")
         reverse = left > right
@@ -3768,19 +3768,19 @@ def set_ylim(self, bottom=None, top=None, emit=True, auto=False,
             # so only grab the limits if we really need them.
             old_bottom, old_top = self.get_ylim()
             if bottom <= 0:
-                cbook._warn_external(
+                _api.warn_external(
                     'Attempted to set non-positive bottom ylim on a '
                     'log-scaled axis.\n'
                     'Invalid limit will be ignored.')
                 bottom = old_bottom
             if top <= 0:
-                cbook._warn_external(
+                _api.warn_external(
                     'Attempted to set non-positive top ylim on a '
                     'log-scaled axis.\n'
                     'Invalid limit will be ignored.')
                 top = old_top
         if bottom == top:
-            cbook._warn_external(
+            _api.warn_external(
                 f"Attempting to set identical bottom == top == {bottom} "
                 f"results in singular transformations; automatically "
                 f"expanding.")
@@ -4067,7 +4067,7 @@ def _set_view_from_bbox(self, bbox, direction='in',
                     xzc + xwidth/2./scl, yzc + ywidth/2./scl]
         elif len(bbox) != 4:
             # should be len 3 or 4 but nothing else
-            cbook._warn_external(
+            _api.warn_external(
                 "Warning in _set_view_from_bbox: bounding box is not a tuple "
                 "of length 3 or 4. Ignoring the view change.")
             return
@@ -4211,7 +4211,7 @@ def format_deltas(key, dx, dy):
                 result = (mtransforms.Bbox(newpoints)
                           .transformed(p.trans_inverse))
             except OverflowError:
-                cbook._warn_external('Overflow while panning')
+                _api.warn_external('Overflow while panning')
                 return
         else:
             return
diff --git a/lib/matplotlib/axes/_secondary_axes.py b/lib/matplotlib/axes/_secondary_axes.py
index d59b6ab8953d..49c968499fe6 100644
--- a/lib/matplotlib/axes/_secondary_axes.py
+++ b/lib/matplotlib/axes/_secondary_axes.py
@@ -1,7 +1,6 @@
 import numpy as np
 
 from matplotlib import _api
-import matplotlib.cbook as cbook
 import matplotlib.docstring as docstring
 import matplotlib.ticker as mticker
 from matplotlib.axes._base import _AxesBase, _TransformedBoundsLocator
@@ -246,7 +245,7 @@ def set_aspect(self, *args, **kwargs):
         Secondary axes cannot set the aspect ratio, so calling this just
         sets a warning.
         """
-        cbook._warn_external("Secondary axes can't set the aspect ratio")
+        _api.warn_external("Secondary axes can't set the aspect ratio")
 
     def set_color(self, color):
         """
diff --git a/lib/matplotlib/axis.py b/lib/matplotlib/axis.py
index 2724cd7b1a02..d4f4da74915d 100644
--- a/lib/matplotlib/axis.py
+++ b/lib/matplotlib/axis.py
@@ -1390,9 +1390,9 @@ def grid(self, b=None, which='major', **kwargs):
                 raise ValueError(
                     "'b' and 'visible' specify inconsistent grid visibilities")
             if kwargs and not b:  # something false-like but not None
-                cbook._warn_external('First parameter to grid() is false, '
-                                     'but line properties are supplied. The '
-                                     'grid will be enabled.')
+                _api.warn_external('First parameter to grid() is false, '
+                                   'but line properties are supplied. The '
+                                   'grid will be enabled.')
                 b = True
         which = which.lower()
         _api.check_in_list(['major', 'minor', 'both'], which=which)
@@ -1604,8 +1604,8 @@ def _set_formatter(self, formatter, level):
         if (isinstance(formatter, mticker.FixedFormatter)
                 and len(formatter.seq) > 0
                 and not isinstance(level.locator, mticker.FixedLocator)):
-            cbook._warn_external('FixedFormatter should only be used together '
-                                 'with FixedLocator')
+            _api.warn_external('FixedFormatter should only be used together '
+                               'with FixedLocator')
 
         if level == self.major:
             self.isDefault_majfmt = False
diff --git a/lib/matplotlib/backend_bases.py b/lib/matplotlib/backend_bases.py
index 6e5896765fc5..c0afddbe25d2 100644
--- a/lib/matplotlib/backend_bases.py
+++ b/lib/matplotlib/backend_bases.py
@@ -3546,7 +3546,7 @@ def show(cls, *, block=None):
             try:
                 manager.show()  # Emits a warning for non-interactive backend.
             except NonGuiException as exc:
-                cbook._warn_external(str(exc))
+                _api.warn_external(str(exc))
         if cls.mainloop is None:
             return
         if block is None:
diff --git a/lib/matplotlib/backend_managers.py b/lib/matplotlib/backend_managers.py
index 951978a3a06a..ada29050b711 100644
--- a/lib/matplotlib/backend_managers.py
+++ b/lib/matplotlib/backend_managers.py
@@ -209,8 +209,8 @@ def update_keymap(self, name, key, *args):
                 key = [key]
             for k in key:
                 if k in self._keys:
-                    cbook._warn_external('Key %s changed from %s to %s' %
-                                         (k, self._keys[k], name))
+                    _api.warn_external(
+                        f'Key {k} changed from {self._keys[k]} to {name}')
                 self._keys[k] = name
 
     def remove_tool(self, name):
@@ -267,8 +267,8 @@ def add_tool(self, name, tool, *args, **kwargs):
             raise ValueError('Impossible to find class for %s' % str(tool))
 
         if name in self._tools:
-            cbook._warn_external('A "Tool class" with the same name already '
-                                 'exists, not added')
+            _api.warn_external('A "Tool class" with the same name already '
+                               'exists, not added')
             return self._tools[name]
 
         tool_obj = tool_cls(self, name, *args, **kwargs)
@@ -437,7 +437,6 @@ def get_tool(self, name, warn=True):
             return name
         if name not in self._tools:
             if warn:
-                cbook._warn_external("ToolManager does not control tool "
-                                     "%s" % name)
+                _api.warn_external(f"ToolManager does not control tool {name}")
             return None
         return self._tools[name]
diff --git a/lib/matplotlib/backend_tools.py b/lib/matplotlib/backend_tools.py
index 7c8a9fbfbfe6..9ce38b98701e 100644
--- a/lib/matplotlib/backend_tools.py
+++ b/lib/matplotlib/backend_tools.py
@@ -80,7 +80,7 @@ class ToolBase:
     """
 
     def __init__(self, toolmanager, name):
-        cbook._warn_external(
+        _api.warn_external(
             'The new Tool classes introduced in v1.5 are experimental; their '
             'API (including names) will likely change in future versions.')
         self._name = name
diff --git a/lib/matplotlib/backends/backend_pdf.py b/lib/matplotlib/backends/backend_pdf.py
index 903d78c7c99c..636f87c3d97b 100644
--- a/lib/matplotlib/backends/backend_pdf.py
+++ b/lib/matplotlib/backends/backend_pdf.py
@@ -210,12 +210,12 @@ def check_trapped(x):
     }
     for k in info:
         if k not in keywords:
-            cbook._warn_external(f'Unknown infodict keyword: {k!r}. '
-                                 f'Must be one of {set(keywords)!r}.')
+            _api.warn_external(f'Unknown infodict keyword: {k!r}. '
+                               f'Must be one of {set(keywords)!r}.')
         elif not keywords[k](info[k]):
-            cbook._warn_external(f'Bad value for infodict keyword {k}. '
-                                 f'Got {info[k]!r} which is not '
-                                 f'{keywords[k].text_for_warning}.')
+            _api.warn_external(f'Bad value for infodict keyword {k}. '
+                               f'Got {info[k]!r} which is not '
+                               f'{keywords[k].text_for_warning}.')
     if 'Trapped' in info:
         info['Trapped'] = Name(info['Trapped'])
 
diff --git a/lib/matplotlib/backends/backend_pgf.py b/lib/matplotlib/backends/backend_pgf.py
index 54f19b7d9c32..2c1eb9de859f 100644
--- a/lib/matplotlib/backends/backend_pgf.py
+++ b/lib/matplotlib/backends/backend_pgf.py
@@ -628,7 +628,7 @@ def draw_image(self, gc, x, y, im, transform=None):
             return
 
         if not os.path.exists(getattr(self.fh, "name", "")):
-            cbook._warn_external(
+            _api.warn_external(
                 "streamed pgf-code does not support raster graphics, consider "
                 "using the pgf-to-pdf option.")
 
diff --git a/lib/matplotlib/backends/qt_editor/_formlayout.py b/lib/matplotlib/backends/qt_editor/_formlayout.py
index c12c93c007cc..e2b371f1652d 100644
--- a/lib/matplotlib/backends/qt_editor/_formlayout.py
+++ b/lib/matplotlib/backends/qt_editor/_formlayout.py
@@ -46,7 +46,7 @@
 import logging
 from numbers import Integral, Real
 
-from matplotlib import cbook, colors as mcolors
+from matplotlib import _api, colors as mcolors
 from matplotlib.backends.qt_compat import QtGui, QtWidgets, QtCore
 
 _log = logging.getLogger(__name__)
@@ -95,7 +95,7 @@ def to_qcolor(color):
     try:
         rgba = mcolors.to_rgba(color)
     except ValueError:
-        cbook._warn_external('Ignoring invalid color %r' % color)
+        _api.warn_external(f'Ignoring invalid color {color!r}')
         return qcolor  # return invalid QColor
     qcolor.setRgbF(*rgba)
     return qcolor
diff --git a/lib/matplotlib/bezier.py b/lib/matplotlib/bezier.py
index e0a9bcc51aa4..1f3ce0b1b24a 100644
--- a/lib/matplotlib/bezier.py
+++ b/lib/matplotlib/bezier.py
@@ -8,7 +8,7 @@
 
 import numpy as np
 
-from matplotlib import _api, cbook
+from matplotlib import _api
 
 
 # same algorithm as 3.8's math.comb
@@ -478,7 +478,7 @@ def get_parallels(bezier2, width):
                                       cmx - c2x, cmy - c2y)
 
     if parallel_test == -1:
-        cbook._warn_external(
+        _api.warn_external(
             "Lines do not intersect. A straight line is used instead.")
         cos_t1, sin_t1 = get_cos_sin(c1x, c1y, c2x, c2y)
         cos_t2, sin_t2 = cos_t1, sin_t1
diff --git a/lib/matplotlib/cbook/__init__.py b/lib/matplotlib/cbook/__init__.py
index c7ca110a0e04..346ae0cf5431 100644
--- a/lib/matplotlib/cbook/__init__.py
+++ b/lib/matplotlib/cbook/__init__.py
@@ -29,8 +29,7 @@
 
 import matplotlib
 from matplotlib import _api, _c_internal_utils
-from matplotlib._api import (
-    warn_external as _warn_external, classproperty as _classproperty)
+from matplotlib._api import classproperty as _classproperty
 from matplotlib._api.deprecation import (
     deprecated, warn_deprecated,
     _deprecate_method_override, _deprecate_privatize_attribute,
@@ -348,8 +347,8 @@ def _local_over_kwdict(
             if out is None:
                 out = kwarg_val
             else:
-                _warn_external('"%s" keyword argument will be ignored' % key,
-                               warning_cls)
+                _api.warn_external(f'"{key}" keyword argument will be ignored',
+                                   warning_cls)
     return out
 
 
diff --git a/lib/matplotlib/colorbar.py b/lib/matplotlib/colorbar.py
index 22e6448debb7..334c55249816 100644
--- a/lib/matplotlib/colorbar.py
+++ b/lib/matplotlib/colorbar.py
@@ -219,7 +219,7 @@
 def _set_ticks_on_axis_warn(*args, **kw):
     # a top level function which gets put in at the axes'
     # set_xticks and set_yticks by ColorbarBase.__init__.
-    cbook._warn_external("Use the colorbar set_ticks() method instead.")
+    _api.warn_external("Use the colorbar set_ticks() method instead.")
 
 
 class _ColorbarAutoLocator(ticker.MaxNLocator):
@@ -721,7 +721,7 @@ def set_ticklabels(self, ticklabels, update_ticks=True):
             if update_ticks:
                 self.update_ticks()
         else:
-            cbook._warn_external("set_ticks() must have been called.")
+            _api.warn_external("set_ticks() must have been called.")
         self.stale = True
 
     def minorticks_on(self):
diff --git a/lib/matplotlib/contour.py b/lib/matplotlib/contour.py
index c030687e3baf..ed92fe532f30 100644
--- a/lib/matplotlib/contour.py
+++ b/lib/matplotlib/contour.py
@@ -827,7 +827,7 @@ def __init__(self, ax, *args,
 
         if self.filled:
             if self.linewidths is not None:
-                cbook._warn_external('linewidths is ignored by contourf')
+                _api.warn_external('linewidths is ignored by contourf')
             # Lower and upper contour levels.
             lowers, uppers = self._get_lowers_and_uppers()
             # Ensure allkinds can be zipped below.
@@ -878,9 +878,10 @@ def __init__(self, ax, *args,
         self.changed()  # set the colors
 
         if kwargs:
-            s = ", ".join(map(repr, kwargs))
-            cbook._warn_external('The following kwargs were not used by '
-                                 'contour: ' + s)
+            _api.warn_external(
+                'The following kwargs were not used by contour: ' +
+                ", ".join(map(repr, kwargs))
+            )
 
     def get_transform(self):
         """
@@ -1111,7 +1112,7 @@ def _process_contour_level_args(self, args):
             levels_in = self.levels[inside]
             if len(levels_in) == 0:
                 self.levels = [self.zmin]
-                cbook._warn_external(
+                _api.warn_external(
                     "No contour levels were found within the data range.")
 
         if self.filled and len(self.levels) < 2:
@@ -1433,8 +1434,7 @@ def _contour_args(self, args, kwargs):
         self.zmin = float(z.min())
         if self.logscale and self.zmin <= 0:
             z = ma.masked_where(z <= 0, z)
-            cbook._warn_external('Log scale: values of z <= 0 have been '
-                                 'masked')
+            _api.warn_external('Log scale: values of z <= 0 have been masked')
             self.zmin = float(z.min())
         self._process_contour_level_args(args)
         return (x, y, z)
diff --git a/lib/matplotlib/dates.py b/lib/matplotlib/dates.py
index b809c50de79a..9ea05832466a 100644
--- a/lib/matplotlib/dates.py
+++ b/lib/matplotlib/dates.py
@@ -1409,7 +1409,7 @@ def get_locator(self, dmin, dmax):
                     break
             else:
                 if not (self.interval_multiples and freq == DAILY):
-                    cbook._warn_external(
+                    _api.warn_external(
                         f"AutoDateLocator was unable to pick an appropriate "
                         f"interval for this date range. It may be necessary "
                         f"to add an interval value to the AutoDateLocator's "
@@ -1448,7 +1448,7 @@ def get_locator(self, dmin, dmax):
         else:
             locator = MicrosecondLocator(interval, tz=self.tz)
             if date2num(dmin) > 70 * 365 and interval < 1000:
-                cbook._warn_external(
+                _api.warn_external(
                     'Plotting microsecond time intervals for dates far from '
                     f'the epoch (time origin: {get_epoch()}) is not well-'
                     'supported. See matplotlib.dates.set_epoch to change the '
diff --git a/lib/matplotlib/figure.py b/lib/matplotlib/figure.py
index 1fdc14297b0d..f677d83d0e33 100644
--- a/lib/matplotlib/figure.py
+++ b/lib/matplotlib/figure.py
@@ -131,7 +131,7 @@ def add(self, key, a):
         a_existing = self.get(key)
         if a_existing is not None:
             super().remove((key, a_existing))
-            cbook._warn_external(
+            _api.warn_external(
                 "key {!r} already existed; Axes is being replaced".format(key))
             # I don't think the above should ever happen.
 
@@ -1294,7 +1294,7 @@ def subplots_adjust(self, left=None, bottom=None, right=None, top=None,
         """
         if self.get_constrained_layout():
             self.set_constrained_layout(False)
-            cbook._warn_external(
+            _api.warn_external(
                 "This figure was using constrained_layout, but that is "
                 "incompatible with subplots_adjust and/or tight_layout; "
                 "disabling constrained_layout.")
@@ -1621,10 +1621,10 @@ def gca(self, **kwargs):
                 if key == ckey and isinstance(cax, projection_class):
                     return cax
                 else:
-                    cbook._warn_external('Requested projection is different '
-                                         'from current axis projection, '
-                                         'creating new axis with requested '
-                                         'projection.')
+                    _api.warn_external('Requested projection is different '
+                                       'from current axis projection, '
+                                       'creating new axis with requested '
+                                       'projection.')
 
         # no axes found, so create one which spans the figure
         return self.add_subplot(1, 1, 1, **kwargs)
@@ -2426,7 +2426,7 @@ def show(self, warn=True):
         try:
             self.canvas.manager.show()
         except NonGuiException as exc:
-            cbook._warn_external(str(exc))
+            _api.warn_external(str(exc))
 
     def get_axes(self):
         """
@@ -2930,7 +2930,7 @@ def __setstate__(self, state):
         restore_to_pylab = state.pop('_restore_to_pylab', False)
 
         if version != _mpl_version:
-            cbook._warn_external(
+            _api.warn_external(
                 f"This figure was saved with matplotlib version {version} and "
                 f"is unlikely to function correctly.")
 
@@ -3192,12 +3192,12 @@ def execute_constrained_layout(self, renderer=None):
 
         _log.debug('Executing constrainedlayout')
         if self._layoutgrid is None:
-            cbook._warn_external("Calling figure.constrained_layout, but "
-                                 "figure not setup to do constrained layout. "
-                                 " You either called GridSpec without the "
-                                 "figure keyword, you are using plt.subplot, "
-                                 "or you need to call figure or subplots "
-                                 "with the constrained_layout=True kwarg.")
+            _api.warn_external("Calling figure.constrained_layout, but "
+                               "figure not setup to do constrained layout. "
+                               "You either called GridSpec without the "
+                               "figure keyword, you are using plt.subplot, "
+                               "or you need to call figure or subplots "
+                               "with the constrained_layout=True kwarg.")
             return
         w_pad, h_pad, wspace, hspace = self.get_constrained_layout_pads()
         # convert to unit-relative lengths
@@ -3240,9 +3240,9 @@ def tight_layout(self, *, pad=1.08, h_pad=None, w_pad=None, rect=None):
         from contextlib import suppress
         subplotspec_list = get_subplotspec_list(self.axes)
         if None in subplotspec_list:
-            cbook._warn_external("This figure includes Axes that are not "
-                                 "compatible with tight_layout, so results "
-                                 "might be incorrect.")
+            _api.warn_external("This figure includes Axes that are not "
+                               "compatible with tight_layout, so results "
+                               "might be incorrect.")
 
         renderer = get_renderer(self)
         ctx = (renderer._draw_disabled()
diff --git a/lib/matplotlib/gridspec.py b/lib/matplotlib/gridspec.py
index 049a13ec922a..704b577099f4 100644
--- a/lib/matplotlib/gridspec.py
+++ b/lib/matplotlib/gridspec.py
@@ -286,7 +286,7 @@ def subplots(self, *, sharex=False, sharey=False, squeeze=True,
         # instead treated as a bool for sharex.  This check should go away
         # once sharex becomes kwonly.
         if isinstance(sharex, Integral):
-            cbook._warn_external(
+            _api.warn_external(
                 "sharex argument to subplots() was an integer.  Did you "
                 "intend to use subplot() (without 's')?")
         _api.check_in_list(["all", "row", "col", "none"],
@@ -490,9 +490,9 @@ def tight_layout(self, figure, renderer=None,
         subplotspec_list = tight_layout.get_subplotspec_list(
             figure.axes, grid_spec=self)
         if None in subplotspec_list:
-            cbook._warn_external("This figure includes Axes that are not "
-                                 "compatible with tight_layout, so results "
-                                 "might be incorrect.")
+            _api.warn_external("This figure includes Axes that are not "
+                               "compatible with tight_layout, so results "
+                               "might be incorrect.")
 
         if renderer is None:
             renderer = tight_layout.get_renderer(figure)
diff --git a/lib/matplotlib/image.py b/lib/matplotlib/image.py
index 9093d225a958..2718d1c25364 100644
--- a/lib/matplotlib/image.py
+++ b/lib/matplotlib/image.py
@@ -416,7 +416,7 @@ def _make_image(self, A, in_bbox, out_bbox, clip_bbox, magnification=1.0,
                     # Cast to float64
                     if A.dtype not in (np.float32, np.float16):
                         if A.dtype != np.float64:
-                            cbook._warn_external(
+                            _api.warn_external(
                                 f"Casting input data from '{A.dtype}' to "
                                 f"'float64' for imshow")
                         scaled_dtype = np.float64
@@ -1580,8 +1580,8 @@ def imsave(fname, arr, vmin=None, vmax=None, cmap=None, format=None,
             # semantics of duplicate keys in pnginfo is unclear.
             if "pnginfo" in pil_kwargs:
                 if metadata:
-                    cbook._warn_external("'metadata' is overridden by the "
-                                         "'pnginfo' entry in 'pil_kwargs'.")
+                    _api.warn_external("'metadata' is overridden by the "
+                                       "'pnginfo' entry in 'pil_kwargs'.")
             else:
                 metadata = {
                     "Software": (f"Matplotlib version{mpl.__version__}, "
diff --git a/lib/matplotlib/legend.py b/lib/matplotlib/legend.py
index 4553a605c67e..ff557816a865 100644
--- a/lib/matplotlib/legend.py
+++ b/lib/matplotlib/legend.py
@@ -28,7 +28,7 @@
 import numpy as np
 
 import matplotlib as mpl
-from matplotlib import _api, cbook, docstring, colors
+from matplotlib import _api, docstring, colors
 from matplotlib.artist import Artist, allow_rasterization
 from matplotlib.cbook import silent_list
 from matplotlib.font_manager import FontProperties
@@ -404,9 +404,9 @@ def __init__(self, parent, handles, labels,
         _lab, _hand = [], []
         for label, handle in zip(labels, handles):
             if isinstance(label, str) and label.startswith('_'):
-                cbook._warn_external('The handle {!r} has a label of {!r} '
-                                     'which cannot be automatically added to'
-                                     ' the legend.'.format(handle, label))
+                _api.warn_external('The handle {!r} has a label of {!r} '
+                                   'which cannot be automatically added to'
+                                   ' the legend.'.format(handle, label))
             else:
                 _lab.append(label)
                 _hand.append(handle)
@@ -744,7 +744,7 @@ def _init_legend_box(self, handles, labels, markerfirst=True):
         for orig_handle, lab in zip(handles, labels):
             handler = self.get_legend_handler(legend_handler_map, orig_handle)
             if handler is None:
-                cbook._warn_external(
+                _api.warn_external(
                     "Legend does not support {!r} instances.\nA proxy artist "
                     "may be used instead.\nSee: "
                     "https://matplotlib.org/users/legend_guide.html"
@@ -1053,7 +1053,7 @@ def _find_best_position(self, width, height, renderer, consider=None):
         _, _, (l, b) = min(candidates)
 
         if self._loc_used_default and time.perf_counter() - start_time > 1:
-            cbook._warn_external(
+            _api.warn_external(
                 'Creating legend with loc="best" can be slow with large '
                 'amounts of data.')
 
@@ -1203,8 +1203,8 @@ def _parse_legend_args(axs, *args, handles=None, labels=None, **kwargs):
     extra_args = ()
 
     if (handles is not None or labels is not None) and args:
-        cbook._warn_external("You have mixed positional and keyword "
-                             "arguments, some input may be discarded.")
+        _api.warn_external("You have mixed positional and keyword arguments, "
+                           "some input may be discarded.")
 
     # if got both handles and labels as kwargs, make same length
     if handles and labels:
diff --git a/lib/matplotlib/mlab.py b/lib/matplotlib/mlab.py
index ff2a9b023f6c..c9ab4a6ec612 100644
--- a/lib/matplotlib/mlab.py
+++ b/lib/matplotlib/mlab.py
@@ -766,9 +766,8 @@ def specgram(x, NFFT=None, Fs=None, detrend=None, window=None,
     if NFFT is None:
         NFFT = 256  # same default as in _spectral_helper()
     if len(x) <= NFFT:
-        cbook._warn_external("Only one segment is calculated since parameter "
-                             "NFFT (=%d) >= signal length (=%d)." %
-                             (NFFT, len(x)))
+        _api.warn_external("Only one segment is calculated since parameter "
+                           f"NFFT (={NFFT}) >= signal length (={len(x)}).")
 
     spec, freqs, t = _spectral_helper(x=x, y=None, NFFT=NFFT, Fs=Fs,
                                       detrend_func=detrend, window=window,
diff --git a/lib/matplotlib/patches.py b/lib/matplotlib/patches.py
index ad144c1b39ce..4d9b36bad463 100644
--- a/lib/matplotlib/patches.py
+++ b/lib/matplotlib/patches.py
@@ -84,7 +84,7 @@ def __init__(self,
         self._fill = True  # needed for set_facecolor call
         if color is not None:
             if edgecolor is not None or facecolor is not None:
-                cbook._warn_external(
+                _api.warn_external(
                     "Setting the 'color' property will override "
                     "the edgecolor or facecolor properties.")
             self.set_color(color)
diff --git a/lib/matplotlib/pyplot.py b/lib/matplotlib/pyplot.py
index 312f8e280ba4..f54597146fd2 100644
--- a/lib/matplotlib/pyplot.py
+++ b/lib/matplotlib/pyplot.py
@@ -304,7 +304,7 @@ class backend_mod(matplotlib.backend_bases._Backend):
 def _warn_if_gui_out_of_main_thread():
     if (_get_required_interactive_framework(_backend_mod)
             and threading.current_thread() is not threading.main_thread()):
-        cbook._warn_external(
+        _api.warn_external(
             "Starting a Matplotlib GUI outside of the main thread will likely "
             "fail.")
 
@@ -745,8 +745,7 @@ def figure(num=None,  # autoincrement if None, else integer from 1-N
         all_labels = get_figlabels()
         if fig_label not in all_labels:
             if fig_label == 'all':
-                cbook._warn_external(
-                    "close('all') closes all existing figures.")
+                _api.warn_external("close('all') closes all existing figures.")
             num = next_num
         else:
             inum = all_labels.index(fig_label)
@@ -758,7 +757,7 @@ def figure(num=None,  # autoincrement if None, else integer from 1-N
     if manager is None:
         max_open_warning = rcParams['figure.max_open_warning']
         if len(allnums) == max_open_warning >= 1:
-            cbook._warn_external(
+            _api.warn_external(
                 f"More than {max_open_warning} figures have been opened. "
                 f"Figures created through the pyplot interface "
                 f"(`matplotlib.pyplot.figure`) are retained until explicitly "
@@ -1213,9 +1212,9 @@ def subplot(*args, **kwargs):
     # intended to be the sharex argument is instead treated as a
     # subplot index for subplot()
     if len(args) >= 3 and isinstance(args[2], bool):
-        cbook._warn_external("The subplot index argument to subplot() appears "
-                             "to be a boolean. Did you intend to use "
-                             "subplots()?")
+        _api.warn_external("The subplot index argument to subplot() appears "
+                           "to be a boolean. Did you intend to use "
+                           "subplots()?")
     # Check for nrows and ncols, which are not valid subplot args:
     if 'nrows' in kwargs or 'ncols' in kwargs:
         raise TypeError("subplot() got an unexpected keyword argument 'ncols' "
@@ -2411,8 +2410,8 @@ def polar(*args, **kwargs):
     # If an axis already exists, check if it has a polar projection
     if gcf().get_axes():
         if not isinstance(gca(), PolarAxes):
-            cbook._warn_external('Trying to create polar plot on an axis '
-                                 'that does not have a polar projection.')
+            _api.warn_external('Trying to create polar plot on an axis '
+                               'that does not have a polar projection.')
     ax = gca(polar=True)
     ret = ax.plot(*args, **kwargs)
     return ret
diff --git a/lib/matplotlib/rcsetup.py b/lib/matplotlib/rcsetup.py
index 60cffd0fb39c..3aa6e898c271 100644
--- a/lib/matplotlib/rcsetup.py
+++ b/lib/matplotlib/rcsetup.py
@@ -167,9 +167,8 @@ def _validate_date_converter(s):
         return
     s = validate_string(s)
     if s not in ['auto', 'concise']:
-        cbook._warn_external(f'date.converter string must be "auto" '
-                             f'or "concise", not "{s}".  Check your '
-                             'matplotlibrc')
+        _api.warn_external(f'date.converter string must be "auto" or '
+                           f'"concise", not "{s}".  Check your matplotlibrc')
         return
     import matplotlib.dates as mdates
     mdates._rcParam_helper.set_converter(s)
diff --git a/lib/matplotlib/sphinxext/mathmpl.py b/lib/matplotlib/sphinxext/mathmpl.py
index 1d7a93ca15b4..b86d0e841c53 100644
--- a/lib/matplotlib/sphinxext/mathmpl.py
+++ b/lib/matplotlib/sphinxext/mathmpl.py
@@ -6,7 +6,7 @@
 import sphinx
 
 import matplotlib as mpl
-from matplotlib import cbook, mathtext
+from matplotlib import _api, mathtext
 
 
 # Define LaTeX math node:
@@ -52,7 +52,7 @@ def latex2png(latex, filename, fontset='cm'):
             depth = mathtext.math_to_image(
                 latex, filename, dpi=100, format="png")
         except Exception:
-            cbook._warn_external(f"Could not render math expression {latex}")
+            _api.warn_external(f"Could not render math expression {latex}")
             depth = 0
     return depth
 
diff --git a/lib/matplotlib/style/core.py b/lib/matplotlib/style/core.py
index 71cd0283e7ae..0c2f632e016a 100644
--- a/lib/matplotlib/style/core.py
+++ b/lib/matplotlib/style/core.py
@@ -19,7 +19,7 @@
 import warnings
 
 import matplotlib as mpl
-from matplotlib import _api, cbook, rc_params_from_file, rcParamsDefault
+from matplotlib import _api, rc_params_from_file, rcParamsDefault
 
 _log = logging.getLogger(__name__)
 
@@ -47,7 +47,7 @@ def _remove_blacklisted_style_params(d, warn=True):
     for key in d:  # prevent triggering RcParams.__getitem__('backend')
         if key in STYLE_BLACKLIST:
             if warn:
-                cbook._warn_external(
+                _api.warn_external(
                     "Style includes a parameter, '{0}', that is not related "
                     "to style.  Ignoring".format(key))
         else:
diff --git a/lib/matplotlib/tests/test_cbook.py b/lib/matplotlib/tests/test_cbook.py
index bc772eba5a96..9fa70d3d87f0 100644
--- a/lib/matplotlib/tests/test_cbook.py
+++ b/lib/matplotlib/tests/test_cbook.py
@@ -346,7 +346,7 @@ def test_warn_external_frame_embedded_python():
     with patch.object(cbook, "sys") as mock_sys:
         mock_sys._getframe = Mock(return_value=None)
         with pytest.warns(UserWarning, match=r"\Adummy\Z"):
-            cbook._warn_external("dummy")
+            _api.warn_external("dummy")
 
 
 def test_to_prestep():
@@ -607,7 +607,7 @@ def test_safe_first_element_pandas_series(pd):
 
 
 def test_warn_external(recwarn):
-    cbook._warn_external("oops")
+    _api.warn_external("oops")
     assert len(recwarn) == 1
     assert recwarn[0].filename == __file__
 
diff --git a/lib/matplotlib/text.py b/lib/matplotlib/text.py
index 1e3a820a2115..c086377c843e 100644
--- a/lib/matplotlib/text.py
+++ b/lib/matplotlib/text.py
@@ -1760,9 +1760,9 @@ def transform(renderer) -> Transform
         if (xytext is None and
                 textcoords is not None and
                 textcoords != xycoords):
-            cbook._warn_external("You have used the `textcoords` kwarg, but "
-                                 "not the `xytext` kwarg.  This can lead to "
-                                 "surprising results.")
+            _api.warn_external("You have used the `textcoords` kwarg, but "
+                               "not the `xytext` kwarg.  This can lead to "
+                               "surprising results.")
 
         # clean up textcoords and assign default
         if textcoords is None:
@@ -1879,7 +1879,7 @@ def update_positions(self, renderer):
             # Ignore frac--it is useless.
             frac = d.pop('frac', None)
             if frac is not None:
-                cbook._warn_external(
+                _api.warn_external(
                     "'frac' option in 'arrowprops' is no longer supported;"
                     " use 'headlength' to set the head length in points.")
             headlength = d.pop('headlength', 12)
diff --git a/lib/matplotlib/ticker.py b/lib/matplotlib/ticker.py
index d740721b6c78..6e8df3d19461 100644
--- a/lib/matplotlib/ticker.py
+++ b/lib/matplotlib/ticker.py
@@ -1714,7 +1714,7 @@ def set_params(self, **kwargs):
         Do nothing, and raise a warning. Any locator class not supporting the
         set_params() function will call this.
         """
-        cbook._warn_external(
+        _api.warn_external(
             "'set_params()' not defined for locator of type " +
             str(type(self)))
 
@@ -2557,7 +2557,7 @@ def nonsingular(self, vmin, vmax):
         if not np.isfinite(vmin) or not np.isfinite(vmax):
             vmin, vmax = 1, 10  # Initial range, no data plotted yet.
         elif vmax <= 0:
-            cbook._warn_external(
+            _api.warn_external(
                 "Data has no positive values, and therefore cannot be "
                 "log-scaled.")
             vmin, vmax = 1, 10
@@ -2852,7 +2852,7 @@ def nonsingular(self, vmin, vmax):
         elif vmax <= 0 or vmin >= 1:
             # vmax <= 0 occurs when all values are negative
             # vmin >= 1 occurs when all values are greater than one
-            cbook._warn_external(
+            _api.warn_external(
                 "Data has no values between 0 and 1, and therefore cannot be "
                 "logit-scaled."
             )
@@ -2917,8 +2917,8 @@ def __init__(self, n=None):
     def __call__(self):
         """Return the locations of the ticks."""
         if self.axis.get_scale() == 'log':
-            cbook._warn_external('AutoMinorLocator does not work with '
-                                 'logarithmic scale')
+            _api.warn_external('AutoMinorLocator does not work with '
+                               'logarithmic scale')
             return []
 
         majorlocs = self.axis.get_majorticklocs()
diff --git a/lib/matplotlib/tight_layout.py b/lib/matplotlib/tight_layout.py
index 6afb55084772..1a1b2a20a359 100644
--- a/lib/matplotlib/tight_layout.py
+++ b/lib/matplotlib/tight_layout.py
@@ -11,7 +11,7 @@
 
 import numpy as np
 
-from matplotlib import cbook, rcParams
+from matplotlib import _api, rcParams
 from matplotlib.font_manager import FontProperties
 from matplotlib.transforms import TransformedBbox, Bbox
 
@@ -134,14 +134,14 @@ def auto_adjust_subplotpars(
             margin_bottom += rel_height + pad_inches / fig_height_inch
 
     if margin_left + margin_right >= 1:
-        cbook._warn_external('Tight layout not applied. The left and right '
-                             'margins cannot be made large enough to '
-                             'accommodate all axes decorations. ')
+        _api.warn_external('Tight layout not applied. The left and right '
+                           'margins cannot be made large enough to '
+                           'accommodate all axes decorations. ')
         return None
     if margin_bottom + margin_top >= 1:
-        cbook._warn_external('Tight layout not applied. The bottom and top '
-                             'margins cannot be made large enough to '
-                             'accommodate all axes decorations. ')
+        _api.warn_external('Tight layout not applied. The bottom and top '
+                           'margins cannot be made large enough to '
+                           'accommodate all axes decorations. ')
         return None
 
     kwargs = dict(left=margin_left,
@@ -154,9 +154,9 @@ def auto_adjust_subplotpars(
         # axes widths:
         h_axes = (1 - margin_right - margin_left - hspace * (cols - 1)) / cols
         if h_axes < 0:
-            cbook._warn_external('Tight layout not applied. tight_layout '
-                                 'cannot make axes width small enough to '
-                                 'accommodate all axes decorations')
+            _api.warn_external('Tight layout not applied. tight_layout '
+                               'cannot make axes width small enough to '
+                               'accommodate all axes decorations')
             return None
         else:
             kwargs["wspace"] = hspace / h_axes
@@ -164,9 +164,9 @@ def auto_adjust_subplotpars(
         vspace = vspaces[1:-1, :].max() + vpad_inches / fig_height_inch
         v_axes = (1 - margin_top - margin_bottom - vspace * (rows - 1)) / rows
         if v_axes < 0:
-            cbook._warn_external('Tight layout not applied. tight_layout '
-                                 'cannot make axes height small enough to '
-                                 'accommodate all axes decorations')
+            _api.warn_external('Tight layout not applied. tight_layout '
+                               'cannot make axes height small enough to '
+                               'accommodate all axes decorations')
             return None
         else:
             kwargs["hspace"] = vspace / v_axes
@@ -289,14 +289,14 @@ def get_tight_layout_figure(fig, axes_list, subplotspec_list, renderer,
         div_row, mod_row = divmod(max_nrows, rows)
         div_col, mod_col = divmod(max_ncols, cols)
         if mod_row != 0:
-            cbook._warn_external('tight_layout not applied: number of rows '
-                                 'in subplot specifications must be '
-                                 'multiples of one another.')
+            _api.warn_external('tight_layout not applied: number of rows '
+                               'in subplot specifications must be '
+                               'multiples of one another.')
             return {}
         if mod_col != 0:
-            cbook._warn_external('tight_layout not applied: number of '
-                                 'columns in subplot specifications must be '
-                                 'multiples of one another.')
+            _api.warn_external('tight_layout not applied: number of '
+                               'columns in subplot specifications must be '
+                               'multiples of one another.')
             return {}
 
         rowNum1, colNum1 = divmod(num1, cols)
diff --git a/lib/matplotlib/transforms.py b/lib/matplotlib/transforms.py
index 1a73ae3d0443..2dc1a8f3d9c7 100644
--- a/lib/matplotlib/transforms.py
+++ b/lib/matplotlib/transforms.py
@@ -229,10 +229,10 @@ class BboxBase(TransformNode):
         @staticmethod
         def _check(points):
             if isinstance(points, np.ma.MaskedArray):
-                cbook._warn_external("Bbox bounds are a masked array.")
+                _api.warn_external("Bbox bounds are a masked array.")
             points = np.asarray(points)
             if any((points[1, :] - points[0, :]) == 0):
-                cbook._warn_external("Singular Bbox.")
+                _api.warn_external("Singular Bbox.")
 
     def frozen(self):
         return Bbox(self.get_points().copy())
@@ -1789,7 +1789,7 @@ def transform_affine(self, points):
             # points to an array in the first place.  If we can use
             # more arrays upstream, that should help here.
             if not isinstance(points, (np.ma.MaskedArray, np.ndarray)):
-                cbook._warn_external(
+                _api.warn_external(
                     f'A non-numpy array of type {type(points)} was passed in '
                     f'for transformation, which results in poor performance.')
             return self._transform_affine(points)
diff --git a/lib/matplotlib/tri/triinterpolate.py b/lib/matplotlib/tri/triinterpolate.py
index 5e6a2ab11888..8c649d5c27fc 100644
--- a/lib/matplotlib/tri/triinterpolate.py
+++ b/lib/matplotlib/tri/triinterpolate.py
@@ -1201,10 +1201,10 @@ def compute_dz(self):
         err0 = np.linalg.norm(Kff_coo.dot(Uf0) - Ff)
         if err0 < err:
             # Maybe a good occasion to raise a warning here ?
-            cbook._warn_external("In TriCubicInterpolator initialization, "
-                                 "PCG sparse solver did not converge after "
-                                 "1000 iterations. `geom` approximation is "
-                                 "used instead of `min_E`")
+            _api.warn_external("In TriCubicInterpolator initialization, "
+                               "PCG sparse solver did not converge after "
+                               "1000 iterations. `geom` approximation is "
+                               "used instead of `min_E`")
             Uf = Uf0
 
         # Building dz from Uf
diff --git a/lib/mpl_toolkits/axes_grid1/inset_locator.py b/lib/mpl_toolkits/axes_grid1/inset_locator.py
index 19f7ccbb1778..4af827e60f47 100644
--- a/lib/mpl_toolkits/axes_grid1/inset_locator.py
+++ b/lib/mpl_toolkits/axes_grid1/inset_locator.py
@@ -2,7 +2,7 @@
 A collection of functions and objects for creating or placing inset axes.
 """
 
-from matplotlib import cbook, docstring
+from matplotlib import _api, docstring
 from matplotlib.offsetbox import AnchoredOffsetbox
 from matplotlib.patches import Patch, Rectangle
 from matplotlib.path import Path
@@ -474,10 +474,9 @@ def inset_axes(parent_axes, width, height, loc='upper right',
     if bbox_transform in [parent_axes.transAxes,
                           parent_axes.figure.transFigure]:
         if bbox_to_anchor is None:
-            cbook._warn_external("Using the axes or figure transform "
-                                 "requires a bounding box in the respective "
-                                 "coordinates. "
-                                 "Using bbox_to_anchor=(0, 0, 1, 1) now.")
+            _api.warn_external("Using the axes or figure transform requires a "
+                               "bounding box in the respective coordinates. "
+                               "Using bbox_to_anchor=(0, 0, 1, 1) now.")
             bbox_to_anchor = (0, 0, 1, 1)
 
     if bbox_to_anchor is None:
diff --git a/lib/mpl_toolkits/axisartist/axislines.py b/lib/mpl_toolkits/axisartist/axislines.py
index 05e1d1cd6ce0..842de4f9a731 100644
--- a/lib/mpl_toolkits/axisartist/axislines.py
+++ b/lib/mpl_toolkits/axisartist/axislines.py
@@ -384,7 +384,7 @@ def new_fixed_axis(self, loc,
                        ):
 
         if axes is None:
-            cbook._warn_external(
+            _api.warn_external(
                 "'new_fixed_axis' explicitly requires the axes keyword.")
             axes = self.axes
 
@@ -404,7 +404,7 @@ def new_floating_axis(self, nth_coord, value,
                           ):
 
         if axes is None:
-            cbook._warn_external(
+            _api.warn_external(
                 "'new_floating_axis' explicitly requires the axes keyword.")
             axes = self.axes
 
diff --git a/lib/mpl_toolkits/axisartist/clip_path.py b/lib/mpl_toolkits/axisartist/clip_path.py
index f12c463b7771..830dc7fa2aa9 100644
--- a/lib/mpl_toolkits/axisartist/clip_path.py
+++ b/lib/mpl_toolkits/axisartist/clip_path.py
@@ -1,12 +1,12 @@
 import numpy as np
 from math import degrees
-from matplotlib import cbook
+from matplotlib import _api
 import math
 
 
 def atan2(dy, dx):
     if dx == 0 and dy == 0:
-        cbook._warn_external("dx and dy are 0")
+        _api.warn_external("dx and dy are 0")
         return 0
     else:
         return math.atan2(dy, dx)
diff --git a/lib/mpl_toolkits/mplot3d/axes3d.py b/lib/mpl_toolkits/mplot3d/axes3d.py
index 5e5d20ea0719..0ff0ca6d7f64 100644
--- a/lib/mpl_toolkits/mplot3d/axes3d.py
+++ b/lib/mpl_toolkits/mplot3d/axes3d.py
@@ -600,7 +600,7 @@ def margins(self, *margins, x=None, y=None, z=None, tight=True):
 
         if x is None and y is None and z is None:
             if tight is not True:
-                cbook._warn_external(f'ignoring tight={tight!r} in get mode')
+                _api.warn_external(f'ignoring tight={tight!r} in get mode')
             return self._xmargin, self._ymargin, self._zmargin
 
         if x is not None:
@@ -759,7 +759,7 @@ def set_xlim3d(self, left=None, right=None, emit=True, auto=False,
             right = old_right
 
         if left == right:
-            cbook._warn_external(
+            _api.warn_external(
                 f"Attempting to set identical left == right == {left} results "
                 f"in singular transformations; automatically expanding.")
         reverse = left > right
@@ -813,7 +813,7 @@ def set_ylim3d(self, bottom=None, top=None, emit=True, auto=False,
             top = old_top
 
         if bottom == top:
-            cbook._warn_external(
+            _api.warn_external(
                 f"Attempting to set identical bottom == top == {bottom} "
                 f"results in singular transformations; automatically "
                 f"expanding.")
@@ -868,7 +868,7 @@ def set_zlim3d(self, bottom=None, top=None, emit=True, auto=False,
             top = old_top
 
         if bottom == top:
-            cbook._warn_external(
+            _api.warn_external(
                 f"Attempting to set identical bottom == top == {bottom} "
                 f"results in singular transformations; automatically "
                 f"expanding.")
@@ -1573,7 +1573,7 @@ def plot_surface(self, X, Y, Z, *args, norm=None, vmin=None,
         if Z.ndim != 2:
             raise ValueError("Argument Z must be 2-dimensional.")
         if np.any(np.isnan(Z)):
-            cbook._warn_external(
+            _api.warn_external(
                 "Z contains NaN values. This may result in rendering "
                 "artifacts.")