$$
f(n) = \begin{cases}
f(n-1) + n(n-1) & \text{if $n>0$ }\\
0 & \text{if $n=0$}
\end{cases}
$$
Prove by induction that for all $n$ belongs to $\mathbb{N}$

$$
f(n) = \sum\limits\_{i=0}^n i^2 - \sum\limits\_{i=0}^n i
$$ 

Base Case: When $n=0$ $f(0) = 0$ and when $n=1$ $f(1) = 0$

Any hints on this? I am not sure how to proceed?