Square Hunting

No general formula for any random/ irregular figure. However, there are some general formulas as follows:-

If there is a $n$ x $n$ square [an array of (n+1)x(n+1) points], then :-

(a) no. of squares within this square = $\sum n^2$

(b) no .of rectangles within this square = $\sum n^3$ $=$ $\sum n$ $.$ $\sum n$

If there is a $m$ x $n$ rectangle [an array of (m+1)x(n+1) points], then :-

(c) no. of squares within this rectangle = $mn+$ $(m-1)(n-1)+$ ... until $(m-x)$ or $(n-x)$ become $1$

(d) no .of rectangles within this rectangle = $\displaystyle \sum_{i=1}^m i$ $\displaystyle \sum_{j=1}^n j$

Are you trying to say that you needed those squares to be confirmed as squares before you would class them as such? Just look at them! Clearly approximate, if not exact, squares - compared to very clear rectangles.