Algebra
Advanced

Sum of First n Cubes

Closed form for the sum of the first n cubes.

Formula

∑k=1nk3=(n(n+1)2)2\sum_{k=1}^{n} k^3 = \left(\frac{n(n+1)}{2}\right)^2

Variables

nUpper limit

Example

1³ + 2³ + 3³ = (3·4/2)² = 6² = 36. ✓

Did You Know?

Amazingly, the sum of the first n cubes equals the square of the sum of the first n numbers.

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