f(x)=x^2/(x-2)^3

is this function odd even or neither?

f(-x) = (-x)^2/((-x)-2)^3 = x^2/(-x-2)^3 = -x^2/(x+2)^3

If even, f(-x) = f(x)
If odd, f(-x) = -f(x).

So, neither even nor odd.