This just didn't work.
I worked out how to arrange the colors in a sort of "Waffle Weave" arrangement, but when I tried it out on a 4x4x4 cube it looked horrible. Really, just look at it!
So I tried again on a 5x5x5, hoping the background color between the stripes might make them more visible. It did, but it still looked awful.
Oh well, I've got better ideas...
[Edit] Patrick C noticed the Waffle pattern is somewhat clearer if you concentrate on just one face at a time. Sure enough! From the angle shown below, the pattern is even visible on the 4x4x4. (If you squint.)
