Sum of cubes in Archimedes way[siu-kái | kái goân-sí-bé]
First part, to decompose each cubic into a sum of squares, then compose them from different direction.
apply it to
To sum these n identities, let
Second part, make use of ; apply it to :
To sum these n identities,
OK, easy part now, to merge the results of first part and second part, we can get
BTW, Archimedes would use at first part, and use at second part.