how many squares?

You've got your basic 16 of the 1x1

Then you have 9 of the 2x2

Then you have 4 of the 3x3

Then you have 1 of the 4x4

16 + 9 + 4 + 1 = 30

There are 30

There is one square in the square you described. I suspect what you really meant was how many squares are in the figure below.

There is one 4x4's,

four 3x3's,

nine 2x2's, and

sixteen 1x1's

for a total of 30 squares.

30?