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Sum Of Cubes Calculator

Work out sum of cubes instantly with clear inputs, formula shown and shareable results.

About Sum Of Cubes Calculator

Remarkably, the sum of the first n cubes is the square of the nth triangular number: 1³ + 2³ + … + n³ = [n(n+1)/2]². So the cubes always add to a perfect square.

Formula

Sum of cubes

1³ + 2³ + … + n³ = [n(n + 1) / 2]²

Worked example

With the default values below, Sum Of Cubes Calculator returns Sum of the first n cubes of 3,025. Change any input above and every figure here is recalculated in your browser.

Inputs used

How many terms naccepts 1–100,000
10
Start fromminimum 1
1

Results

Sum of the first n cubes
3,025
nth triangular number
55
Sum of n cubes from your start value
3,025
Largest cube in the sum
1,000

Step by step

  1. 1Values used
  2. 2Sum of cubes
  3. 3Sum of the first n cubes= 3,025
  4. 4nth triangular number= 55
  5. 5Sum of n cubes from your start value= 3,025
  6. 6Largest cube in the sum= 1,000

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What is 1³ + 2³ + … + 10³?

(10 × 11 / 2)² = 55² = 3025.

Why does a square appear?

Because each cube k³ can be split into consecutive odd numbers, and the odd numbers themselves sum to perfect squares.

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Sum Of Cubes Calculator – Calculate Sum of the first n cubes