To determine if the function is even, odd, or neither, replace the x in the function with -x. If the result is f(-x)=f(x), the function is even. If it is f(-x)=-f(x), the function is odd. Otherwise, the function is neither even nor odd.
So, replacing the x with -x in the given function yields,
Notice that the denominator changes from (x-2)^3 to (x+2)^3. This means that f(-x) is not equal to the original function f(x). It is not also equal to -f(x).
Hence, the given function is neither even nor odd.