Taking into account the perturbative corrections of Einstein (EN)-Maxwell gravity, we study thermodynamical behavior of the black holes in the context of geometrical thermodynamics (GT). We consider a quadratic Maxwell invariant as a correction of Maxwell theory in electromagnetic viewpoint and Gauss-Bonnet (GB) gravity as a correction of EN theory in gravitational point of view. We study thermodynamical phase transition and show that employing Weinhold, Ruppeiner and Quevedo approaches fails to produce desirable results. Next, Hendi-Panahiyan-Eslam Panah-Momennia (HPEM) metric will be employed in order to study GT of the solutions. We show that this metric is capable of matching all the divergence points of its thermodynamical curvature scalar with phase transition and bound points. Moreover, the effects of the variation of different parameters on phase transition points will be investigated.