Orthogonal Pinstripes

Possibly the simplest pattern for the even-numbered cubes, Pinstripes requires only 4 moves on a 2x2x2 and only 8 moves on a 4x4x4. Only 12 moves would be required on a 6x6x6 cube.

A similar-looking pattern can be arranged on the 5x5x5, but it's based on a different principle.

Cube-in-Cube

The Cube-in-Cube is one of the few patterns that can be adapted to all orders of puzzle cubes: Rubik's Cube, Rubik's Revenge, Meffert's Master Cube, Rubik's Wahn, et cetera.

In fact, there are a variety of options for the higher order cubes. Should the smaller cube be 2x2 or 3x3? Or even 4x4 (on the 5x5)? Take your pick.

I used Eastsheen cubes for the 2x2x2, 4x4x4, and 5x5x5 in the illustration and a Famwealth 3x3x3 that had a similar color scheme on the red-yellow-blue faces. The colors on the 3x3 don't quite match on the reverse side, as shown below.

2x2 Twist

Very few patterns are possible on the 2x2 puzzle cubes because there are only 8 parts, each of which can be deflected into 3 orientations. 8 doesn't divide evenly into 3.

This "pattern" demonstrates the problem rather clearly. I had to arrange it with two slightly different patterns, depending on which side you view it from. One side includes an extra twist of one of the corners.