Now that you know how we can represent a 4D cube in 3D, we look at a rotation in 4 dimensions:

You might understand how to solve a rubik’s cube in 4D:
http://www.superliminal.com/cube/cube.htm
You can use the program online or download it to your computer and have hours of fun with it. The makers of the program were so friendly to mention me in their hall of fame on the 121st place after I had solved the cube.
http://www.superliminal.com/cube/halloffame.htm

Let’s go over to the 5th dimension or what about 7 dimensions…
http://www.gravitation3d.com/magiccube5d/
http://astr73.narod.ru/MC7D/MC7D.html