If you divide any square into power (2, 2N) equal squares then total number of squares formed is sigma(power(i,2)) where i iterates from 1 to power( 2, N).

E.g

1 square has total 1,

Divided into 4 has total 1^2 +2^2

Divided into 16 equal squares has total 1^2 + 2^2 + 3^2 + 4^2

Divided into 64 equal squares has 1^2 + 2^2 + 3^2 + ......... + 8^2

Can you prove if this is correct? I have solved it.