How to solve a 4x4x4, 5x5x5 Rubik's cube, or higher


Here are some basic principles:
Since on larger than 3x3x3 cubes, there is a parity problem, solving those cubes in an efficient manner requires to do it in a different order than what is usually done for the 3x3x3.
If you try to solve a 4x4x4 starting with centers, then edges and finish with the corners, you can end up in a situation where you have just 2 centers to swap, which is not possible to have on a 3x3x3. In order to solve that situation, you will need to rotate a face 1/4 turn (which basically swaps 4 centers and 4 sets of edges), then resolve the edges and the corners.
Likewise, you may end up with a situation where you have just 2 edges to swap. To solve this you will need to rotate a middle slice by 1/4 turn, then resolve the edges and the centers.

So, to avoid having to do some double work, I suggest that you proceed this way:

First make a face using any method you want.
Then make the opposite face, starting by placing the corners, then the edges and the centers.
Then, place the remaining edges on the 2 central slices.
Then, place the the remaining centers.

Below are a series of algorithms to help you swap edges and center pieces. These are just examples. There are many variations for each
algorithm. Feel free to experiment to find the one you need. A simple variation is to do the algorithm in reverse order. Make sure you reverse the direction of each rotation too.



Exchanging edges without changing anything else

swap 3 edges			swap 6 edges
-T R T 2R -R -T -R T R -2R	D -R -D -2R R D R -D -R 2R	D2 B R2 -B 2R2 R2 B R2 -B 2R2 R2 D2	-T R T 3R -R -T -R T R -3R	-T R T 2R -R 4R -3R -T -R T R -2R 3R -4R
2 sides 10 moves	2 sides 10 moves	3 sides 12 moves	2 sides 10 moves	2 sides 14 moves

Exchanging centers without changing anything else

swap 3 center pieces			swap 6 center pieces
2R -R T 3R -2R -T R -2R T 2R -3R -T	3R -2R T 2R -R -T 2R -3R T R -2R -T	2R2 -R2 T 3R2 -2R2 -T 2R2 -R2 T 3R2 -2R2 -T	2R -R T 4R -2R -T R -2R T 2R -4R -T	2R -R T 5R -4R 3R -2R -T R -2R T 4R -5R 2R -3R -T
2 sides 12 moves	2 sides 12 moves	2 sides 12 moves	2 sides 12 moves	2 sides 16 moves

Click here if you need to understand the notation used on this page