<image> In a Cartesian coordinate system, we call points with integer x and y coordinates as lattice points. It is stipulated that the interior of the square does not include points on the boundary. Observe the square centered at the origin with one side parallel to the x-axis as shown in the figure: There is 1 lattice point inside the square of side length 1, 1 lattice point inside the square of side length 2, 9 lattice points inside the square of side length 3, ..., then the number of lattice points inside the square of side length 8 is _____.