I made several different versions of this image, but this is the most convoluted one. I have used a construction similar to this one in the past, but always with tetrahedral units, not with cubical ones. Or, at least they started out cubical before I started hacking at them and twisting them around.
My original goal for this construction was to remove enough of the material of the cube units so that none of the individual components were touching each other in the final construction. Later, I went back and twisted the vertices around and stretched the exposed points to fill in some of the gaps.