You cannot efficiently cool a cubical CPU.

Take eight chips. Stack them, insert spacers and bridges from top to bottom, and connect them via BGA or pins or what-have-you on the very top and very bottom chips.

Now turn them sideways, so they rest on the edges. Put the stack in a small ceramic container with copper bottom and top. Fill with a high efficiency thermal transfer fluid, and make sure the convection currents flow properly.

There you go, small matter of engineering.

This defeats the "shorter distance in a cube" issue.

Not yet.

CPUs are already 3 dimensional, the 'wiring' connecting the transistors is often several layers think.