[Summation of numerical sequences and series of differences]

Output the formula for the sum $1^{3}+2^{3}+3^{3}+\ldots+n^{3}$.
Find the sequence $a_{\mathrm{n}}$ of the form $a_{n}=A n^{4}+B n^{3}+C n^{2}+D n$, for which $\Delta a_{n}=n^{3}$.

## Answer

$\left(\frac{n(n+1)}{2}\right)^{2}$