if you know MI of a sheet{rect or square} , then choose a elementry sheet and intigrate its MI.

Moment of Inertia about edge

Where L is the length of the side.

Use Parallel axis Theorem.(Shift it along the diagonal of the square element).

 but ans is     

The answer which I have given is for side length L..

In your question if the length is 2L then the answer will obviously by substituting 'L'  (i.e Length) in my eqn. by 2L you will get the answer as (8ML^2)/3