Good game!
It was a good game, but a few minor changes could have improved it greatly.
First of all, instead of having the solved cube disappear, you should allow the player to analyze it if they choose; don't change the level until the user presses a 'next' button.
Secondly, after beating a game like this, the player should be rewarded -the ending you provided was hardly rewarding!
Third, there should be some way to select levels -perhaps a password system?
Other than that, perfect puzzle game.
Thanks for the game, I enjoyed it.