Do the differences of perfect squares apply to perfect cubes and more? I'm curious about a special property of squares. The difference between perfect squares starting from 0 are 1,3,5,7,9..., where each difference goes up by 2. I want to know if there are any patterns for perfect cubes or quartics. Are the differences in a pattern of some sort?

For cubes $$\begin {array} &0&&1&&8&&27&&64&&125\\&1&&7&&19&&37&&61\\&&6&&12&&18&&24\\&&&6&&6&&6 \end {array}$$  Try it yourself for quartics.  What do you find?
