No it cannot be done.
Each rectangle covers one white square and one black square, because on a chess board the white and black squares are always adjacent.
The two squares which we remove from the chess board are the same colour, and so the remaining board has two more boxes of one colour than the other.
And after the rectangles have covered 60 boxes, there will be left two squares of the same colour.
Obviously the remaining rectangles cannot cover these two squares.