Matching preclusion originates from the measurement of interconnection network robustness in the event of edge failure. Conditional matching preclusion belongs to generalized matching preclusion. We obtain the matching preclusion number and conditional matching preclusion number for hierarchical cubic network( $HC{N}_n$). Additionally, all the optimal (conditional) matching preclusion sets of $HC{N}_n$ are characterized, which generalize some related results of Birgham et al. and Cheng et al.