This came of watching Brun's video on YouTube (I highly recommend his channel):
Turns out (not a pun) this is a classic puzzle presented to machinists:
The challenge in this exercise was in trying to come up with a model suitable for 3D printing. Approached this as first as might a machinist - carving out cylinders from the nested cubes, but quickly realized the inside surface of the cubes was not ideal. Had to bump up my CAD game, slightly, to get a spherical inside surface. :)
This is in fact a superior result practical with 3D printing that is not practical with subtractive manufacture. Either the inner cubes are not free to move, or the interior of the cube is not a sphere.
(Some guy with a fancy CAM lathe might prove me slightly wrong. Perhaps my nephew.)
Designed in OnShape: