How much data could I store on a Rubik's Cube?
If you consider the cube as living in a physical space, then you can get an extra factor of 24 from its orientation: assume it's sitting on a table and note the uppermost face (six options) and the face that's facing north (four more options). That gives you $\lfloor \log_2 (24\times 43\ 252\,...)\rfloor = 69\,\text{bits}$, and you could get even more by considering more fine-grained notions of orientation, at the risk of losing information by somebody jostling the cube.