Sum of the first 506 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 506 square numbers, you ask? Here we will give you the formula to calculate the first 506 square numbers and then we will show you how to calculate the first 506 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 506 square numbers, we enter n = 506 into our formula to get this:

		506(506 + 1) × (2(506) + 1)
		6

First, calculate each section of the numerator: 506(506 + 1) equals 256542 and (2(506) + 1) equals 1013. Therefore, the problem above becomes this:

		256542 × 1013
		6

Next, we calculate 256542 times 1013 which equals 259877046. Now our problem looks like this:

		259877046
		6

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

259877046 ÷ 6 = 43312841

There you go. The sum of the first 506 square numbers is 43312841.

You may also be interested to know that if you list the first 506 square numbers 1, 2, 9, etc., the 506th square number is 256036.

Sum of Square Numbers Calculator
Need the answer to a similar problem? Get the first n square numbers here.

What is the sum of the first 507 square numbers?
Here is the next math problem on our list that we have explained and calculated for you.