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Sum of Cubes from 1 to n Calculator

Σ k³ = (n·(n + 1) / 2)².

Compute the closed-form sum of the first n positive cubes: 1³ + 2³ + ⋯ + n³ = (n·(n+1)/2)² = (Σk)². Note that the sum of cubes equals the square of the sum of the first n integers — a beautiful classical identity.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

Σₖ₌₁ⁿ k³ = (n·(n+1)/2)².

In depth

Compute the closed-form sum of the first n positive cubes: 1³ + 2³ + ⋯ + n³ = (n·(n+1)/2)² = (Σk)². Note that the sum of cubes equals the square of the sum of the first n integers — a beautiful classical identity.