Multiplexing a cude 4x4x4=64 RGB would yield the same number of RGB LED's as Tower of 8x8=64 RGB. What I offered is a lot more powerful and can easily be expanded with software and plugged in modules without a lot of fuss.
But if one wants to pursue the multiplexing method: You need 16bits (Base of 4x4) x 3bits (RGB) x 4bits (High or levels) = 4 x 4 x 4 RGB LED Cube. I have not looked that such project but I would persume that they used a 16bit LED driver, multiplexed 4, scanned (multiplexed) 3 for RGB.