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Sum of cubes calculator

Add up cubes fast: the sum of the first n cubes (1³+2³+…+n³, which equals the square of the n-th triangular number), the cubes over a range n₁³…n₂³, or the cubes of your own list of numbers. Exact integer arithmetic, however large.

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Enter Mode, n₁ (start), n₂ (end) / n, Custom numbers and the Sum of cubes calculator works out Sum of cubes, Terms summed straight away. For instance, with Mode = Range n₁³…n₂³, n₁ (start) = 1, n₂ (end) / n = 10 and Custom numbers = 2, 3, 5, 7 it returns Sum of cubes = 3,025 and Terms summed = 10.

How to use it

  1. Enter your values: Mode, n₁ (start), n₂ (end) / n, Custom numbers.
  2. Read the result instantly: Sum of cubes, Terms summed.

Frequently asked questions

What does the Sum of cubes calculator actually compute?

It takes Mode, n₁ (start), n₂ (end) / n and Custom numbers and derives Sum of cubes and Terms summed from them. The calculation is live as you type, so the result updates on every change.

What information do I need to provide?

4 values: Mode, n₁ (start), n₂ (end) / n and Custom numbers. Nothing else is required — no account, no file upload.

Can you show a worked example?

With Mode = Range n₁³…n₂³, n₁ (start) = 1, n₂ (end) / n = 10 and Custom numbers = 2, 3, 5, 7, the calculator returns Sum of cubes = 3,025 and Terms summed = 10. Those figures come from running this exact tool, so you can reproduce them by entering the same values.

What happens if I enter larger values?

It moves a lot. Using Mode = First n cubes, n₁ (start) = 2, n₂ (end) / n = 20 and Custom numbers = 2, 3, 6, 8 instead, Sum of cubes goes from 3,025 to 44,100 — which is why it is worth testing a few scenarios rather than trusting a single figure.

Which “Mode” option should I choose?

You can pick between « Range n₁³…n₂³ », « First n cubes » and « Custom list ». Each one changes what the calculator works out, so switch and compare — the default is « Range n₁³…n₂³ ».

What does it give for smaller values?

Scaled down to Mode = Range n₁³…n₂³, n₁ (start) = 1, n₂ (end) / n = 5 and Custom numbers = 2, 3, Sum of cubes comes out at 225. The relationship is worth checking at both ends before you rely on a single result.

When would I actually use this?

Reading a number written another way: a Roman numeral on a monument, a hexadecimal colour, a binary byte, or a fraction that needs reducing.

What is the most common mistake?

Assuming a decimal fraction survives a change of base. A tenth is exact in decimal and infinitely repeating in binary, which is why 0.1 + 0.2 is not 0.3 in most programming languages.

What is the difference between the Sum of cubes calculator and the Sum calculator?

This one returns Sum of cubes and Terms summed; the Sum calculator returns Sum and Count. That is the whole difference — open the one whose figure you need.

Is there a tool for the next step?

Sum of positive integers calculator is the closest one after this: The sum of all whole numbers from n₁ to n₂ in one step — Gauss's trick, n₂(n₂+1)/2 − (n₁−1)n₁/2, instead of adding them one by one. From 1 to 100 is the classic 5050; works for any range and any size.

Further reading

All guides →
How-toHow to Round Numbers: Round Half Up, Round Half to Even, and MoreRound to any decimal place or number of significant figures, and learn when to use round half up versus round half to even to avoid bias.ExplainerSignificant Figures Explained: Counting, Rounding, and Why They MatterLearn what counts as a significant figure, the rules for leading, trailing, and captive zeros, and how sig figs keep your calculated answers honest.How-toHow to Find Prime Factors: Factor Trees and the Division MethodBreak any whole number into its prime building blocks with a factor tree or repeated division — and write the result as a clean prime factorization with exponents.How-toHow to Multiply and Divide Fractions: Multiply Across, Flip to DivideMultiplying fractions needs no common denominator — just multiply across. Dividing means multiplying by the reciprocal. Learn both with worked examples and how to simplify.How-toHow to Add and Subtract Fractions: Common Denominator, Combine, SimplifyYou can only add or subtract fractions that share a denominator. Learn to find a common denominator, combine the numerators, and simplify the result, with a worked example.How-toHow to Do Long Division: Divide, Multiply, Subtract, Bring DownLong division breaks a big division into a repeating four-step cycle. Learn the divide-multiply-subtract-bring-down loop and how to read the remainder, with a worked example.