Prove that: For all n is an element of Z (n is an integer): n is even implies that (n^3)-8 is even?

Let n be an even integer. This means n = 2q for some integer, q. N^3 - 8 = (2q)^3 - 8 = 8q^3 - 8 = 2(4q^3 - 4) which is even Therefore, for all even integers, n, n^3 - 8 is even.

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