Puzzle ZRZL 

Workings

Hint
How many 2 x 2 squares are there?

Answer
There are 128 squares without a rook.

Reasoning
There are 62 squares of size 1 x 1.
There are 41 squares of size 2 x 2.
There are 18 squares of size 3 x 3.
There are  6 squares of size 4 x 4.
There is   1 square  of size 5 x 5.

Giving a total of 62 + 41 + 18 + 6 + 1 = 128 squares.