Soma de Cubos 1³ até n³
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
S = [n(n+1)/2]²
About this calculator
The sum of cubes calculator computes the result of adding the cubes of the first n natural numbers: 1³ + 2³ + 3³ + ... + n³. It uses the formula S = [n(n+1)/2]², providing the exact value quickly and accurately.
To use the calculator, simply enter the value of n (a positive integer) and click calculate. The result is displayed instantly. The formula derives from a known mathematical property: the sum of cubes equals the square of the sum of the first n numbers.
This calculator is useful for math students, engineers, and professionals working with number sequences. For example, when studying progressions or solving summation problems in algebra, the tool saves time and prevents manual errors.
Caution: the formula only works for positive natural numbers (n ≥ 1). For very large n, the result can be huge; the calculator handles large numbers, but ensure the input is an integer. Also, note that the sum is from 1³ to n³, not other ranges.
Frequently asked questions
What does summing cubes mean?
Summing cubes means calculating 1³ + 2³ + 3³ + ... + n³, i.e., raising each natural number from 1 to n to the third power and adding all results.
Does the formula work for n = 0?
No, the formula is valid only for n ≥ 1. For n = 0, the sum is 0, but the formula would give 0² = 0, so it works, but the typical context is for positive natural numbers.
Can I use decimal numbers?
No, the calculator expects a positive integer. The formula applies to natural numbers, not decimals.
What is the difference between sum of cubes and sum of squares?
The sum of cubes uses the formula [n(n+1)/2]², while the sum of squares (1²+2²+...+n²) uses n(n+1)(2n+1)/6. They yield different results.
Why is the result always a perfect square?
Because the formula is the square of the sum of numbers from 1 to n, which is an integer. Thus, the result is always a perfect square.