I'm kind of exagerrating the scores but this is...
GREAT!. I'm stumped on lvl 16 at the moment, on the few levels before that I ended up either rerouting or randomly envisioning 'highlighted' paths through the cube which help out a bit. There tends to be a lot of 'only room for 1 path' choke points, or mainly a single one per level in the levels after lvl 12 or so. I guess this is the basic rubix cube layout to make it difficult and you mainly end up finding it purely by chance or by thinking so much you suddenly see it.
I am busy trying to come up with a formula to hopefully give me an easy way out :). It might work. Anyways keep up the good work and next game make it SIX sides for increased difficulty :<(),
nice work on this, One of the reviews said this was a copy of some hyper cube thing but even if it is it's fun and is a good thinking game :), keep it up!.