Sum of First N Cubes Calculator

How it is calculated

The sum of the first n cubes is 1³ + 2³ + … + n³ = (n(n+1)/2)². First the tool finds the nth triangular number T = n(n+1)/2 (the sum 1 + 2 + … + n), then squares it. Both T and the sum are shown with thousands separators. n must be a whole number from 1 to 13,776: decimals such as 5.5, zero and negatives give no result, and so does anything above 13,776, because the square would no longer be exactly representable and the digits shown could be wrong. For n = 13,776 the sum is 9,005,246,260,992,576. The cubes start at 1³, so 0³ is not part of the sum, and only consecutive cubes from 1 are covered, not arbitrary cubes.

Common mistakes

• Squaring n(n+1) and forgetting to halve it first; that gives a result four times too large.
• Confusing this with the sum of the first n squares, which has a different formula, n(n+1)(2n+1)/6; for n = 10 that sum is 385, not 3,025.
• Entering n as a decimal or with a unit; the tool accepts only whole numbers.
• Using it for cubes that do not start at 1³ or skip terms (for example only odd numbers); the identity covers consecutive cubes from 1³ to n³ only.
• Entering the last cube (1000) instead of n (10); n is the count of terms and the largest base, not the last cube.