What can be assembled from stickerless disassemblable cubes?

[IoriYagami]

In case you didn't know, many of chinese stickerless cubes can be disassembled into pieces, so that each corner piece is in 3 single color parts, each edge in 2 parts, and so on for other puzzles.
I tried playing around my cube, and so far just made a weird shifted color puzzle, where top and bottom are standart and each side is color-shifted 1 square to the left (or right, just the same). It naturally has parity, because of those green-green, red-red, etc edges, and ambiguity on the bottom layer (is it shifted to left or right?) pic in attachment

So what other fun puzzles can be created?
You can also get more than one cube to get more colored parts, you know. Heh, 6 cubes will make you a solid-color fool's cube always solved (not that it's much fun, but cute nonetheless).

 

[Damien Porter]

My favorite mod is a simple 3 colour cube. Using 2 cubes just ensure that opposite faces are the same colour.

You can also use 5 to make a cube similar to the illusion. 2 colours in a checker board pattern on every face. One of the faces is inverted.