"I wonder if the guy Will Smith played in The Pursuit of Happyness can create a formula to solve it?"

I am not a pro in mathematic. But I think if someone really would do a formula for the usual cube (which someone sure did) using it on a biger cube with more colours and more buttons/objects would be no problem for them ~him I guess. The reason behind mathematical formulas is exactly to solve such problems where you have so big numbers and so many different variables that you cant solve it succesfully with trial & error anymore ;)