Squared triangular number

In number theory, the sum of the first n cubes is the square of the nth triangular number. That is,

${\displaystyle 1^{3}+2^{3}+3^{3}+\cdots +n^{3}=\left(1+2+3+\cdots +n\right)^{2}.}$

The same equation may be written more compactly using the mathematical notation for summation:

${\displaystyle \sum _{k=1}^{n}k^{3}=\left(\sum _{k=1}^{n}k\right)^{2}.}$

This identity is sometimes called Nicomachus's theorem, after Nicomachus of Gerasa (c. 60 – c. 120 CE).