I modified the program to change colors each time it completes the cycle.
There are 2 version of the color cycle program, version cycles through:
Red
Blue
Green
Yellow
Purple
Teal
White
Version 2 is more like a color wheel, or rainbow where colors
Yellow
Red
Purple
Blue
Teal
Green
It could be easily modified to do random color(max 7 colors). each cycle.
Getting more colors will be difficult, there really isnt hardware PWM support (there is, but only on a few pins, not enough for the whole cube) This cube is directly connected, not serialized, so you cant do SPI. I think you can get some color mixing, but its not too simple.
TransCubeColorcycle2.ino (16 KB)
TransCubeColorcycle1.ino (16 KB)