If I want to find the sum of a series that is = x^2, how can I do it without adding each individual element?

For example, with linear series, you take the lowest and highest values (at the beginning and end) to get the average, then multiply by the number of elements. I've been trying to figure out one for

1^2+2^2 + 3^2 + ... n^2

but keep hitting dead ends. Care to help?