This is based on 4^3=64. And since 64^4=16777216, there are 4 levels of cube within cube. I skipped over 3 levels, because it requires one at 2^12 and two at 2^6, and so lacks a certain iterational symmetry, let's say. But this one is the most cube levels you can also arrange into a square. I will probably do the three level image after deciding on the ideal configuration.