>>10878848So a lot of the techniques you use to solve the 3x3x3 you can also use to solve major elements of the others
However, the 4x4x4 introduces some new complications, which require their own formulas. The extra edge pieces, and the center pieces (the center pieces are really easy).
The 5x5x5 can be solved using the exact same formulas as the 4x4x4, except it introduces just ONE new complication (that is, it is possible for two edge pieces to be switched for each other, with nothing else different about the cube).
Solving this was the hardest part by far. The others took me a week or so, this one took me months of fiddling around.
I'm trying to picture in my mind of the 6x6x6 or 7x7x7 will introduce yet new complications that cannot be addressed with these formulas, and I can't think how they would. It's very hard to visualize.