Like a BOSS.
I mean, srsly, think about it. What if the external Rubik's cube shifted every few minutes, but within, there is a central axis cube/sphere (whatever rests at the center of a regular Rubik's Cube), where we could move around, not subject to the cube's shifting, and interact with one another.
What's more, the thing could be the size of Jupiter, so there's enough room for us all. And it could have guardians or sentries, which would naturally be reality benders of at least mid-level caliber.
“…Judge not what a man has done, but judge what he could have done if he was a different bloke altogether. For art thou a leper? And a leper can changeth his spots…” --Rudy Wade, Misfits (Series 4, Episode 8)