qua patet orbis

We all know that the first \(n\) odd numbers sum to \(n^2\):

1 == 1^2

[1] TRUE

1 + 3 == 2^2

[1] TRUE

1 + 3 + 5 == 3^2

[1] TRUE

1 + 3 + 5 + 7 == 4^2

[1] TRUE

This extension to the same property amazes me even more:

2^3 == 3 + 5

[1] TRUE

3^3 == 7 + 9 + 11

[1] TRUE

#...
7^3 == 43 + 45 + 47 + 49 + 51 + 53 + 55

[1] TRUE