Your conception of a ball bouncing in a color cube is interesting. Because you are cycling by 10 among 256 choices, your R will always be odd and your G will always be even so you don't hit every color. Cycling by evens through evens maintains parity. However, your B will hit every value eventually. As for corners, we'd need R=255, G=0, and B=255 OR B=0. However, whenever R is 255, G is always 246, because these values move antiparallel to each other.
Nice! What if all three values were relatively prime to 256, and relatively prime to each other? Kind of a neat math question. Imagine starting at 0,0,0 and having adding numbers of 3, 5 and 7 for example. We could even use "wraparound" (mod 256) to simplify it. Will every value (r,g,b) be reached?