Solution to Recurrence Relation I asked a question previously, about how to describe 
$$
f(n) = n^3
$$
As a recurrence relation. I was, quite rightly, given $a_1=1$ and $a_{n+1}=a_n+3n^2+3n+1$.
I have attempted to solve it, using forward substitution, but I'm having trouble.
I started out by assuming a solution to this recurrence relation was $n^3$. I then attempted a proof by induction that $a_n + 2 = (n+1)^3$
And now I am stuck out of my mind! Can anyone help me out here?

$$a_{n+1}=(n+1)^3=n^3+3n^2+3n+1=a_n+3n^2+3n+1$$
