Sum of Cubes of First n Natural Numbers

There are several mathematics patterns available that students study in their curriculum. One of the popular patterns is the Sum of Cubes of First n Natural Numbers. If you have no knowledge about what is the cube of a number, just understand that any number that is multiplied three times by itself is called the cube of a number. For instance 23 =8. It means 222 =8. As there are many natural numbers in mathematics just imagine what could be an exact figure if you sum up all cubes of the natural numbers.

In linear algebra this phenomena also works. Thus, it is recommended to follow this guide to know about how to calculate the sum of n natural numbers. Keep reading.

Natural numbers in simpler terms are normal counting numbers that go from the start to infinity. To calculate the sum of first n natural numbers means you have to calculate the cubes from 1 till infinity. For beginners, calculating cubes of the first 5, 10 and 20 natural numbers will be easier. They can simply do multiplication and add them.

But don’t you think it is a too lengthy process? It is because numbers are going till infinity. See readers, the sum of first five natural numbers will be expressed as 13 + 23 + 33 + 43 + 53 and if you talk about the first 10 natural numbers cubes, it will be like 13 + 23 + 33 + 43 + 53 + 63 + 73 + 83 + 93 + 103, and so on.

Do you want us to make it simpler? Here are some examples that show the sum of cubes of n natural numbers.

The Sum of cubes of the first 2 natural numbers that is 1 and 2 is expressed as 13 + 23 = 1 + 8 which equals 9.

The Sum of cubes of the first 3 natural numbers 1, 2 and 3 is 13 + 23 + 33 which equals 1 + 8 + 27 = 36.

The Sum of cubes of the first 4 natural numbers 1, 2, 3, and 4 will be 13 + 23 + 33 + 43 = 1 + 8 + 27 + 64 equals to 100.

It looks like a very lengthy process? Don’t you think so? If we keep adding more natural number cubes, it will be a challenging task to calculate all their cube numbers. Therefore, you need a simple formula that helps you in calculating the sum of n natural numbers. Only pick that formula to substitute values and make the calculation process easier.

What is the formula of calculating the cubes of n natural numbers?

If you are dealing with the numerical series having values like 13 + 23 + 33 + 43 + … + n3, the calculation formula to find the sum is.

(n(n+1)/2)2

In this formula n depicts the total natural numbers that start from 1. Now, as you have understood about how to calculate the formula of n natural numbers. It is the time for you to practice and hone your mathematical ability. Use this formula whenever required like in competitive exams or other sums. It saves your time and you don’t require more challenges.

If you want to know whether this formula is correct or not, you can try calculations on your own to derive the same formula. Using this formula students can get good marks. Also,, this formula is used in several questions also. So, don’t ignore it.