Coding is actually used to REDUCE collinearity. But coding can only do so much. My graphs may not be the best way to illustrate, but consider this:
X1 X1^2 X1^3
100 10000 1000000
100 10000 1000000
200 40000 8000000
200 40000 8000000
150 22500 3375000
There is a correlation between X1 and X1^2 (0.997). But if you code to -1, +1, the correlation will drop to 0. This does not happen when cubing because, as you pointed out, -1^3 = +1 and +1^3 = 1, but the correlation on the original scale is large, too.
Dan Obermiller