How to animate a cube with images on their faces?

Question

From this code, how could I animate (speed given by the user) this cube at random so that each face shows me a different image.

EDIT(The idea is that the cube rotates at random and shows different images on each face, it is understood now :(

 $Graphics3D[
 GraphicsComplex[
 Tuples[{0, 1}, 3],
 MapThread[
 {Texture[
 Graphics[ImportString[ExportString[#1, "PDF"], "PDF"][[1, 1]],       Background -> #3]],
 Polygon[#2, VertexTextureCoordinates -> {{0, 0}, {1, 0}, {1, 1}, {0, 1}}]} &,
{Characters["ABCDEF"],
 {{1, 2, 4, 3}, {1, 5, 6, 2}, {1, 3, 7, 5}, {8, 6, 5, 7}, {8, 7, 
   3, 4}, {8, 4, 2, 6}},
 Table[Hue[i/6], {i, 6}]}
]
   ],
 Lighting -> "Neutral"]$

here some example image to put on the faces

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Answer 1

Update 5: In newer versions (e.g., version 13.3.1) replace ImportString[ExportString[#1, "PDF"], "PDF"][[1, 1]] below with

ImportString[ExportString[#, "PDF"], {"PDF", "PageGraphics"}, 
  "TextMode" -> "Outlines"][[1, 1]]

Update 4: Rotations around x axis followed by rotations around y axis followed by rotations around z axis:

faces = Polygon[#, VertexTextureCoordinates -> {{0, 0}, {1, 0}, {1, 1}, {0,  1}}] & /@ 
  {{1, 2, 4, 3}, {1, 5, 6, 2}, {1, 3, 7, 5}, {8, 6, 5, 7}, {8, 7, 3, 4}, {8, 4, 2, 6}};

images = Import /@ 
 {"https://images-na.ssl-images-amazon.com/images/I/51ZQiVNDYPL._SX425_.jpg",
  "https://images-na.ssl-images-amazon.com/images/I/51S7cvjbrqL._SX425_.jpg", 
  "https://images-na.ssl-images-amazon.com/images/I/61acUMNLNvL._SX425_.jpg", 
  "https://images-na.ssl-images-amazon.com/images/I/51xRMocaTKL._SX425_.jpg"};

{one, six} = Texture[Graphics[
      ImportString[ExportString[#1, "PDF"], "PDF"][[1, 1]], 
      Background -> #2]] & @@@ Transpose[{{"1", "6"}, {Red, Yellow}}];
textures2 = Join[Texture /@ images, {one, six}];

Animate[Graphics3D[
  Rotate[GraphicsComplex[Tuples[{0, 1}, 3],Transpose[{textures2, faces}]], t, 
   IdentityMatrix[3][[1 + Quotient[t, 2 Pi]]], {1, 1, 1}/2], 
  Lighting -> "Neutral", SphericalRegion -> True, 
  PlotRange -> {{-1/2, 3/2}, {-1/2, 3/2}, {-1/2, 3/2}}, 
  Boxed -> False], {t, Range[0, 6 Pi - Pi/120, Pi/120]}]

Update 3: Rotations by a random angle around a randomly selected axis:

Animate[Graphics3D[Rotate[GraphicsComplex[Tuples[{0, 1}, 3], 
     Transpose[{textures, faces}]], t, RandomChoice[IdentityMatrix[3]]], 
   Lighting -> "Neutral",  SphericalRegion -> True,  Boxed -> False],
 {t, RandomSample[Range[0, 2 Pi, Pi/60]]}]

frames2 = Table[Graphics3D[
    Rotate[GraphicsComplex[Tuples[{0, 1}, 3], Transpose[{textures, faces}]], t, 
     RandomChoice[IdentityMatrix[3]]], Lighting -> "Neutral", 
     SphericalRegion -> True,  Boxed -> False],
  {t, RandomSample[Range[0, 2 Pi, Pi/60]]}];

Export["cube2.gif", frames2]

Update 2: Rotating a cube with images on its faces:

faces = Polygon[#, VertexTextureCoordinates -> {{0, 0}, {1, 0}, {1, 1}, {0, 1}}] & /@
  {{1, 2, 4, 3}, {1, 5, 6, 2}, {1, 3, 7, 5}, {8, 6, 5, 7}, {8, 7, 3, 4}, {8, 4, 2, 6}};

images = Import /@ 
  {"https://images-na.ssl-images-amazon.com/images/I/51ZQiVNDYPL._SX425_.jpg", 
 "https://images-na.ssl-images-amazon.com/images/I/51S7cvjbrqL._SX425_.jpg", 
 "https://images-na.ssl-images-amazon.com/images/I/61acUMNLNvL._SX425_.jpg", 
 "https://images-na.ssl-images-amazon.com/images/I/51xRMocaTKL._SX425_.jpg"};

{one, six} = Texture[Graphics[
      ImportString[ExportString[#1, "PDF"], "PDF"][[1, 1]], 
      Background -> #2]] & @@@ Transpose[{{"1", "6"}, {Red, Yellow}}];
textures2 = Join[Texture /@ images, {one, six}];

Animate[Graphics3D[
  GraphicsComplex[Tuples[{0, 1}, 3], Transpose[{textures2, faces}]], 
  Lighting -> "Neutral", 
  ViewVector -> 6 { Cos[t], Sin[t], 3 Sin[t]/6 + 1/12}, 
  SphericalRegion -> True], {t, 0, 2 Pi, Pi/60}]

You can control the speed using the second and third buttons.

See also: this answer by halirutan to a related question

Update: Using some of the images from the links in OP:

images = Import /@ 
  {"https://images-na.ssl-images-amazon.com/images/I/51ZQiVNDYPL._SX425_.jpg", 
 "https://images-na.ssl-images-amazon.com/images/I/51S7cvjbrqL._SX425_.jpg", 
 "https://images-na.ssl-images-amazon.com/images/I/61acUMNLNvL._SX425_.jpg", 
 "https://images-na.ssl-images-amazon.com/images/I/51xRMocaTKL._SX425_.jpg"};

{one, six} = Texture[Graphics[
      ImportString[ExportString[#1, "PDF"], "PDF"][[1, 1]], 
      Background -> #2]] & @@@ Transpose[{{"1", "6"}, {Red, Yellow}}];

Just wrap your images with Texture (and add the missing 1 and 6):

textures2 = Join[Texture /@ images, {one, six}];


frames = Table[Graphics3D[GraphicsComplex[Tuples[{0, 1}, 3], 
     Transpose[{RandomSample[textures2, 6], faces}]], Lighting -> "Neutral"], {30}];
ListAnimate[frames]

Original answer:

textures = Texture[Graphics[ImportString[ExportString[#1, "PDF"], "PDF"][[1, 1]], 
      Background -> #2]] & @@@ 
   Transpose[{CharacterRange["A", "Z"], Hue[#/26] & /@ Range[26]}];

faces = Polygon[#, VertexTextureCoordinates -> {{0, 0}, {1, 0}, {1, 1}, {0, 1}}] & /@
  {{1, 2, 4, 3}, {1, 5, 6, 2}, {1, 3, 7, 5}, {8, 6, 5, 7}, {8, 7, 3, 4}, {8, 4, 2, 6}};

frames = Table[Graphics3D[GraphicsComplex[Tuples[{0, 1}, 3], 
    Transpose[{RandomSample[textures, 6], faces}]], Lighting -> "Neutral"], {30}]

ListAnimate[frames]

Export["cube.gif", frames]