Sum of the first 80 square numbers

We define square numbers as numbers that when squared will equal a whole number. Thus, the list of the first square numbers starts with 1, 4, 9, 16, and so on.

What is the sum of the first 80 square numbers, you ask? Here we will give you the formula to calculate the first 80 square numbers and then we will show you how to calculate the first 80 square numbers using the formula.

The formula to calculate the first n square numbers is displayed below:

		n(n + 1) × (2(n) + 1)
		6

To calculate the sum of the first 80 square numbers, we enter n = 80 into our formula to get this:

		80(80 + 1) × (2(80) + 1)
		6

First, calculate each section of the numerator: 80(80 + 1) equals 6480 and (2(80) + 1) equals 161. Therefore, the problem above becomes this:

		6480 × 161
		6

Next, we calculate 6480 times 161 which equals 1043280. Now our problem looks like this:

		1043280
		6

Finally, divide the numerator by the denominator to get our answer:

1043280 ÷ 6 = 173880

There you go. The sum of the first 80 square numbers is 173880.

You may also be interested to know that if you list the first 80 square numbers 1, 2, 9, etc., the 80th square number is 6400.

Sum of Square Numbers Calculator
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