Also, a thing that might not seem immediately obvious to most but is obvious to me given the amount of maths videos I watch on YouTube is that if you add consecutive odd numbers together, you get the square numbers.

So the second difference of the square numbers (i.e. the difference between consecutive odd numbers) is always 2.

The third difference of the cube numbers is always 6 (= 3 x 2 x 1):

1, 8, 27, 64, 125, 216, 343, 512, 729, 1000 -> 7, 19, 37, 61, 91, 127, 169, 217, 271 -> 12, 18, 24, 30, 36, 42, 48, 54 -> 6, 6, 6, 6, 6, 6, 6.

The fourth difference of the fourth powers is always 24 (= 4 x 3 x 2 x 1); and so on.