# How do you find the sum of consecutive cubes?

## How do you find the sum of consecutive cubes?

“The sum of n consecutive cubes is equal to the square of the sum of the first n numbers.” In other words, according to Example 1: 13+23+33+… +n3=n2(n+1)24.

How do you find the sum of the cubes of n natural numbers?

The sum of cubes of n natural numbers means finding the sum of a series of cubes of natural numbers. It can be obtained by using a simple formula S = [n2 (n + 1)2]/4, where S is the sum and n is the number of natural numbers taken.

### What can you say about the sum of consecutive perfect cubes starting with 1?

Therefore, the difference of those squares — each cube — will be a sum of consecutive odd numbers, although not starting with 1. Again, the sum of those four cubes is equal to the square of the fourth triangle….The sum of consecutive cubes.

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32 − 12 = 23.
62 − 32 = 33.
102 − 62 = 43.
152 − 102 = 53.

What is the sum of the 1st cube number?

Is there a formula to add a sequence of cubes? It seems that the sum is always square, but what is even more remarkable is that the sum of the first n cubes, 13+23+… + n 3 = ( n ( n +1)/2)2, which is the square of the n th triangle number.

#### What is the sum of first 10 perfect cubes?

What is the Sum of all Perfect Cubes from 1 to 10? The sum of all perfect cubes from 1 to 10 is 9 i.e. 1 + 8 = 9.

What is the sum of cubes?

Sum or Difference of Cubes A polynomial in the form a 3 + b 3 is called a sum of cubes. A polynomial in the form a 3 – b 3 is called a difference of cubes.

## Why sum of cubes is square of sum?

Inspired by the fact that the sum of the cubes of the first n naturals is equal to the square of their sum, we explore, for each n, the Diophantine equation representing all non-trivial sets of n integers with this property.

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What is the sum of first cube number and third cube number?

The 1st cube number is 1 (1x1x1) and the 3rd cube number is 27 (3x3x3). The sum of 27 and 1 is 28. Hope this helped you!

13.