## Interesting Number Pattern-What is it called?

First off, I play Dungeons and Dragons, which means I often deal with squared numbers due to the way item cost increases.
So, despite being terrible at math, eventually something clicks.
This is that something.
If you take the square of a number, find the difference between it and square of the next number on the number line and then find out the difference between the square of the latter number and the square of the *next* further, you'll find that the difference between squares increased by two.
This has worked with every whole number I've thrown at it, including absurdly big ones where I typed out the initial number at random.
To put it more simply, 1 x1=1 and 2x2=4, a difference of 3. But 3 x 3 is 9, which is 5 more than 4, and 5 is 2 more than the difference between 1² and 2², 3. It works for every three whole number sequence so far.
I am willing to bet it also works with decimals, only not two but two n-ths. I know it works with orders of magnitude, like 100, 200 and 300, again not two but two followed by some zeroes.
Now, what have I found here?
Who discovered it first?
Because I know it isn't me, who didn't even pass Grade 8 math.