t = ImageResize[ExampleData@#, {100, 100}] & /@
   ExampleData["ColorTexture"][[;; 6]];

vtc = {{0, 0}, {1, 0}, {1, 1}, {0, 1}};
coords = {{{0, 0, 0}, {0, 1, 0}, {1, 1, 0}, {1, 0, 0}}, {{0, 0,
     0}, {1, 0, 0}, {1, 0, 1}, {0, 0, 1}}, {{1, 0, 0}, {1, 1, 0}, {1,
     1, 1}, {1, 0, 1}}, {{1, 1, 0}, {0, 1, 0}, {0, 1, 1}, {1, 1,
     1}}, {{0, 1, 0}, {0, 0, 0}, {0, 0, 1}, {0, 1, 1}}, {{1, 0,
     1}, {1, 1, 1}, {0, 1, 1}, {0, 0, 1}}};

Graphics3D[{Table[{Texture@t[[i]],
     Polygon[coords[[i]], VertexTextureCoordinates -> vtc]}, {i, 6}]}]

cubemap = ImageResize[#, Scaled[0.5]] &@ Import@"http://i.stack.imgur.com/hSCfz.jpg";

vtccm = {{##}, {# + 1, #2}, {# + 1, #2 + 1}, {#, #2 + 1}} & @@@ {{1,
      1}, {0, 2}, {1, 2}, {2, 2}, {3, 2}, {1, 3}}/4;

α = 0.;
Graphics3D[{EdgeForm[], Texture[cubemap],
  Polygon[coords, VertexTextureCoordinates -> vtccm]},
 Lighting -> {{"Ambient", White}}, Boxed -> False, ViewAngle -> 1,
 ViewCenter -> {1, 1, 1}/2,
 ViewVector -> {1, 1, 1}/2 + {Cos[α], Sin[α], 0}/8,
 RotationAction -> "Clip", ImageSize -> 500,
 ViewVertical -> {0, 0, 1}]