As my understanding, the "stiffness" extracted is actually (rho*L^{d-1}) for square lattice or 3d simple cubes. The real one should be 2.2427/5 in your case.
But I have a question about the stiffness as well. I used a 8x8x2 lattice, how is the simulated "stiffness" related to the actual one? (if it is 8x8x8, I know it is rho*8, but this is not a simple cubic, is there an expression to calculated it?)