The greatest mathematician in all of antiquity, Archimedes, found you could add up the first n square numbers with a relatively simple formula:

$\displaystyle \frac{{{n}{\left({n}+{1}\right)}{\left({2}{n}+{1}\right)}}}{{6}}={1}^{{2}}+{2}^{{2}}+{3}^{{2}}+\ldots+{n}^{{2}}$

Use this fact to find the sum of the first 22 square numbers.

Answer: The sum of the first 22 square numbers is

Archimedes

(Source: http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Archimedes.html)