Squared triangular number

Nicomachus theorem

1^3 + 2^3 + \cdots + n^3 = (1 + 2 + \cdots + n)^2

Simply put, you can think of it as calculating the volume of a cube by multiplying a 2-dimensional value by another 2-dimensional value. When generalized,

Faulhaber’s formula

The Nicomachus theorem is a special case of Faulhaber's formula when p=3

\sum_{k=1}^n k^p \;=\; \frac{1}{p+1} \sum_{j=0}^{p} \binom{p+1}{j}\,B_j\,n^{\,p+1-j}.

Squared triangular number

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

https://en.wikipedia.org/wiki/Squared_triangular_number

Squared triangular number

Nicomachus theorem

Faulhaber’s formula

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