Here’s an applet for a 4D Rubik’s Cube. The creators also offer some explanation and description of the puzzle and how to solve it. Apparently, there are 1 756 772 880 709 135 843 168 526 079 081 025 059 614 484 630 149 557 651 477 156 021 733 236 798 970 168 550 600 274 887 650 082 354 207 129 600 000 000 000 000 possible states in the 4D cube.