How many squares are there in 8*8 chess board ?



The answer which strikes in the mind at the first instance is 64, (8*8) . I spoke to my self and thought it is so easy, but after some time, I said no! there might be more . I tried to visualize them as shown in the picture below. 

Starting from 1 square unit  (from one corner A) 1*1,then counting the number of squares in 2*2 square unit (taking 2 squares in each direction horizontally and vertically) which is 4 and similarly number of squares in 3*3 square unit is 9 and so on.

 At the end, to find the total number of squares in 8*8 square unit  I added them as 1+4+9+16+25+36+49+64=204.So there are 204 squares in 8*8 chessboard.


To extend this puzzle ,i will ask them if they can apply the same method to find the number of squares in 9*9  square board.