prove that if n is a positive integer, the (7^n)-1 is divisible by 6

Question

prove that if n is a positive integer, the (7^n)-1 is divisible by 6

Answer 1

in general, xⁿ - 1 = (x-1)(x^n-1 + x^n-2 + ... + 1)

and when x=7, that first (linear) factor must be 6.   Q.E.D.