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Sum of Cubes Formula
publish date: 2026/05/23 05:43:44.515008 UTC
Enter the closed-form formula for \(\displaystyle\sum_{k=1}^{n} k^3 = 1^3 + 2^3 + 3^3 + \cdots + n^3\).
Correct Answer
$\frac{n^2(n+1)^2}{4}$
Explanation
The sum of cubes formula is \(\sum k^3 = \frac{n^2(n+1)^2}{4}\). Notably, this equals \(\left(\sum k\right)^2 = \left(\frac{n(n+1)}{2}\right)^2\), an elegant result showing that the sum of the first \(n\) cubes equals the square of the sum of the first \(n\) natural numbers.
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012