  Motivated by the string corrections on the gravity and electrodynamics sides,
we consider a quadratic Maxwell invariant term as a correction of the Maxwell
Lagrangian to obtain exact solutions of higher dimensional topological black
holes in Gauss-Bonnet gravity. We first investigate the asymptotically flat
solutions and obtain conserved and thermodynamic quantities which satisfy the
first law of thermodynamics. We also analyze thermodynamic stability of the
solutions by calculating the heat capacity and the Hessian matrix. Then, we
focus on horizon-flat solutions with adS asymptote and produce a rotating
spacetime with a suitable transformation. In addition, we calculate the
conserved and thermodynamic quantities for asymptotically adS black branes
which satisfy the first law of thermodynamics. Finally, we perform
thermodynamic instability criterion to investigate the effects of nonlinear
electrodynamics in canonical and grand canonical ensembles.
