  Employing two classes of nonlinear electrodynamics, we obtain topological
black hole solutions of Gauss-Bonnet gravity. We investigate geometric
properties of the solutions and find that there is an intrinsic singularity at
the origin. We investigate the thermodynamic properties of the asymptotically
flat black holes and also asymptotically adS solutions. Using suitable local
transformation, we generalize static horizon-flat solutions to rotating ones.
We discuss their conserved and thermodynamic quantities as well as the first
law of thermodynamics. Finally, we calculate the heat capacity of the solutions
to obtain a constraint on the horizon radius of stable solutions.
