I understand the process in calculating a simple series like this one
$$\sum_{n=0}^4 2n$$
but I do not understand the steps to calculate a series like this one
$$\sum_{n=1}^x n^2$$
I have an awesome calculator and know how to use it, so I know the solution
$$\frac{x^3}{3} + \frac{x^2}{2} + \frac{x}{6}$$
but I don't know the steps. All the explanations I find (like those on Purple Math) are for summations like the first one I listed. If someone can provide a detailed explanation on how to calculate a summation like mine or provide a link to one it would be much appreciated.