how many squares are formed when n parallel lines intersect m other parallel lines?

let $n<m$ .
the number of squares of any sizes that can be formed is:
= square of sizes 1 + 2+3+.......+n units
$$\begin{gathered} =nm+(n-1)(m-1)+(n-2)(m-2)+...............+(n-n+1)(m-n+1) \\ ={\sum }_{r=1}^n (n-r+1)(m-r+1) \end{gathered}$$

hope this helps you