We propose a mechanism to engineer an n-photon blockade in a nonlinear cavity with an n-photon parametric drive lambda(adagger n + an). When an n-photon-excitation resonance condition is satisfied, the presence of n photons in the cavity suppresses the absorption of the subsequent photons. To confirm the validity of this proposal, we study the n-photon blockade in an atom-cavity system, a Kerr-nonlinear resonator, and two-coupled Kerrnonlinear resonators. Our results demonstrate that n-photon bunching and (n + 1 )-photon antibunching can be simultaneously obtained in these systems. This effect is due both to the anharmonic energy ladder and to the nature of the n-photon drive. To show the importance of the drive, we compare the results of the n-photon drive with a coherent (one-photon) drive, proving the enhancement of antibunching in the parametric-drive case. This proposal is general and can be applied to realize the n-photon blockade in other nonlinear systems.