Calculate definite integral (4x^2) using definition as a limit of approximating sums

Evaluate $\displaystyle \int_0^4 4x^2 \mathrm{d}x$ by using its definition as a limit of approximating sums.

I can easily calculate the target answer which is 256/3. But I'm having trouble solving it the way the problem asks:

Limit of approximating sums is:

$\displaystyle \lim\limits_{n \to \infty} \sum\limits_{j=1}^n f(c_j) (x_j - x_{j - 1}) = \lim\limits_{n \to \infty} \sum\limits_{j=1}^n f(\frac{4j}{n}) \frac{4}{n} = \lim\limits_{n \to \infty} \sum\limits_{j=1}^n \frac{4^3j^2}{n^2} \frac{4}{n} = 256 \lim\limits_{n \to \infty} \sum\limits_{j=1}^n \frac{j^2}{n^3}$

At that point I'm stuck. Any tips?