17 squares.
1 of size 4x4, 4 of size 3x3, 9 of size 2x2, 16 of size 1x1 Total 30 but that depends on a particular interpretation of the question (16 squares arranged in a 4x4 group). If the 16 are arranged in a row, then they might be regarded as a rectangle and you only have 1 square (the box). If you define the box to be a real 3 dimensional box then the box itself has 6 or 5 squares depending on if it has a lid or not.
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In a square made up of sixteen smaller squares, there are a total of 30 squares. This includes the one large square, the sixteen smaller squares, nine squares formed by combining four smaller squares, and four squares formed by combining nine smaller squares. Each of these squares contributes to the total count of 30 squares within the larger square.
9 *snicker* trick question.
It depends on the size of the squares!
81
16 30 (if you count the squares of all sizes)