In this paper we have added Maxwell, Maxwell-Chern-Simons and gravitational Chern-Simons terms to Born-Infeld extended new massive gravity and we have found different types of (non)extremal charged black holes. For each black hole we find mass, angular momentum, entropy and temperature. Since our solutions are asymptotically $AdS$ or warped-$AdS$, we infer central charges of dual CFTs by using Cardy's formula. Computing conserved charges associated to asymptotic symmetry transformations confirms calculation of central charges. For CFTs dual to asymptotically $AdS$ solutions we find left central charges from Cardy's formula, while conserved charge approach gives both left and right central charges. For CFTs dual to asymptotically warped-$AdS$ solutions, left and right central charges are equal when we have Maxwell-Chern-Simons term but they have different values when gravitational Chern-Simons term is included.

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