I don't think it is possible to color the faces of a single cuboid differently (other than the two sides of one face), though there are multiple methods to create multicolored cuboid-like objects.
Creating multiple polygons:
v = {{-1, -1, -1}, {1, -1, -1}, {1, 1, -1}, {-1, 1, -1}, {-1, -1,
1}, {1, -1, 1}, {1, 1, 1}, {-1, 1, 1}};
idx = {{1, 2, 3, 4}, {1, 2, 6, 5}, {2, 3, 7, 6}, {3, 4, 8, 7}, {4, 1,
5, 8}, {5, 6, 7, 8}};
Graphics3D[Table[{Glow@Hue[i/6], Polygon[v[[idx[[i]]]]]}, {i, 6}], Lighting -> None]

Using textures, from the help on Texture:
sides = Graphics[{Hue@#, Rectangle[]}, ImageSize -> 50] & /@
Most@Range[0, 1, 1/6];
vtc = {{0.01, 0.01}, {0.99, 0.01}, {0.99, 0.99}, {0.01, 0.99}};
Graphics3D[{Black, EdgeForm[Black],
Table[{Texture[sides[[i]]],
GraphicsComplex[v, Polygon[idx[[i]], VertexTextureCoordinates -> vtc]]}, {i, 6}]}]
