"prove for all integers n, that is even. state the proof technique you have used. justify each step in your proof."

i can work it out in my head that it must be, as n cubed will be even if n is even, and odd if n is odd. an even minus an even is still an even, an odd minus an odd is an even. but i can only prove that the equation is a multiple of 3? i'm using proof by induction.