Comment by deruta

And a proof by "counting something":

1 + 2 + ... + n = n(n+1)/2

2 divides n(n+1), n(n+1) = 2m

7 * n^3 + n =

2*(3*n^3 + n) + n^3 - n =

2*(3*n^3 + n) + n(n+1)(n-1) =

2*(3*n^3 + n + m(n-1))