[vikingerik]

There are 43 quintillion cube states, so "trillions" is understating by at least a factor of 10^6.

I'm not sure if the 43 quintillion are reachable in a loop of that many moves, or if you need to backtrack through some states to reach others and thus need more moves than that.

[hvdijk]

"Trillion" has two meanings. I'm Dutch, we use the traditional meaning of 10^18, what you call quintillion :)