Sum of the first 264 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 264 square numbers, you ask? Here we will give you the formula to calculate the first 264 square numbers and then we will show you how to calculate the first 264 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 264 square numbers, we enter n = 264 into our formula to get this:

		264(264 + 1) × (2(264) + 1)
		6

First, calculate each section of the numerator: 264(264 + 1) equals 69960 and (2(264) + 1) equals 529. Therefore, the problem above becomes this:

		69960 × 529
		6

Next, we calculate 69960 times 529 which equals 37008840. Now our problem looks like this:

		37008840
		6

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

37008840 ÷ 6 = 6168140

There you go. The sum of the first 264 square numbers is 6168140.

You may also be interested to know that if you list the first 264 square numbers 1, 2, 9, etc., the 264th square number is 69696.

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