Sum of Cubes Calculator

How it is calculated

Enter n, the number of terms: the tool adds the cubes of the whole numbers from 1 to n. Instead of looping, it first finds the triangular number s = n(n + 1) / 2 (the plain sum 1 + 2 + … + n) and then squares it, so 1³ + 2³ + … + n³ = s². n must be a whole number of at least 1; zero, negatives and decimals return no result. The answer is a single integer shown with thousands separators. Because only n is needed, a limit of 100,000 is as instant as a limit of 10.

Common mistakes

• Squaring n(n + 1) without halving it first. For n = 10 that gives 12,100, which is four times too big; the halved value 55 must be squared.
• Confusing the sum of cubes 1³ + 2³ + … + n³ with a single cube such as n³, or with the sum of squares, which has a different formula.
• Entering the largest base as a power, for example typing 1000 meaning "10³". The field expects how many consecutive cubes to add (n = 10), not the last cube.
• Using the tool for a sum that skips terms, such as only even or odd bases; it always adds every integer from 1 to n.