# Two Quick Combinatorial Proofs of $$\sum_{k=1}^n k^3= \left ( \begin{array}{cc} n+1 \\ 2 \end{array} \right )^2$$

by Arthur T. Benjamin (Harvey Mudd College) and Michael E. Orrison (Harvey Mudd College)

College Mathematics Journal
November, 2002

Subject classification(s): Discrete Mathematics

Two proofs of the equality between the sum from $$1$$ to $$n$$ of $$k^3$$ and $$\frac{n^2 (n+1)^2}{4}$$.

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