7. (10 points) The difference in area between two squares is 2016 square centimeters. If the side lengths of such pairs of squares are both integer centimeters, then how many pairs of squares satisfy the above condition.
12
【Analysis】Assuming the side length of the larger square is $x$, and the smaller square is $y$, we have $x^{2}-y^{2}=(x+y)(x-y)=2016$, $x+y$ and $x-y$ have the same parity, and since the product 2016 is even, they must both be even. Factorizing 2016 gives $2016=2^{5} \times 3^{2} \times 7$, and then solve accordingly.
【Solution】Solution: Assuming the side length of the larger square is $x$, and the smaller square is $y$, from the problem we get:
$$
x^{2}-y^{2}=2016 \text {, }
$$

Factorizing: $(x+y)(x-y)=2016$,
$x+y$ and $x-y$ have the same parity, and since the product 2016 is even, they must both be even,
$$
2016=2^{5} \times 3^{2} \times 7,
$$
The number of factors of 2016: $(1+5) \times(2+1) \times(1+1)=36$ (factors),
There are a total of $36 \div 2=18$ pairs of factors,
Among them, the odd factors are: $(2+1) \times 2=6$ pairs,
So the even numbers are: $18-6=12$ pairs,
That is, there are 12 pairs of squares that satisfy the above conditions.
Therefore, the answer is: 12.