So many numbers

Consider the above 8 $\times$ 8 grid. How many ways are there to write a single digit (0, 1, ..., 8, 9) in each square such that the sum of all the numbers in any 3 $\times$ 3 section is even. If you think the number of ways to fill in this grid with these restrictions is $x$ , type in the number of factors of $x$ (including 1 and $x$ ).

Note: Rotations and reflections are considered to be distinct possibilities.