Algorithms and Rubik's cubes?

I bought a 4x4x4 Rubik's cube because I mastered the 3x3x3 in under 1 minute. I was just wondering if the algorithms for Rubik's cubes with even numbered sides were all similar to other Rubik's with even numbered sides (e.g. a 4x4x4 compared to a 6x6x6). Same thing for cubes with odd numbered sides (e.g. 3x3x3 compared to a 5x5x5). Even Rubik's cubes don't have a center piece and odd ones do, so this has to affect the algorithms in some way, right?