SMO 2010 Problem 2

Let $(a_n), (b_n)$ , $n = 1,2,...$ be two sequences of integers defined by $a_1 = 1, b_1 = 0$ and for $n \geq 1$ $a_{n+1} = 7a_n + 12b_n + 6$ $b_{n+1} = 4a_n + 7b_n + 3$ Prove that $a_n^2$ is the difference of two consecutive cubes.