How many 1 by 1 squares are there on a checkerboard? 2 by 2? 3 by 3? ..
A systematic way of counting the squares can be helpful. You can use this Polypad to help organize your thoughts.
To help you count the number of 2 by 2 squares in any given square, create a transparent 2x2 square and drag it over the sides of the main square. Then a 3x3, a 4x4, and so on.
What did you realize?
For the 8 by 8 checkerboard:
The total number of squares is the sum of the first eight square numbers.
More on the Checkerboard problem
How many cubes are there in an 8x8x8 cube such as this?
If you like this puzzle, try this one!