Beryllium forms stable sandwich and inverse sandwich complexes with the cyclobutadiene molecule. Two types of multidecker complexes are designed. Multidecker inverse sandwiches are found to be thermally more stable than the corresponding sandwich complexes. The average distance between two consecutive metals and the two consecutive cyclobutadiene rings increase gradually on increasing size of the chosen inverse sandwich complexes. The density functional theory functionals B3LYP, BHHLYP, BLYP, M06, CAM-B3LYP, and B2PLYP in conjunction with the 6-311++G (d, p) basis set have been employed for calculating the third-order electric response properties of the chosen beryllium-cyclobutadiene complexes and the results obtained for each functional are found to have a consistent trend. Compared to the normal sandwich compounds the second-hyperpolarizability of inverse sandwiches is predicated to be larger, which fairly correlates with the extent of ground-state polarization. The significant enhancement of cubic polarizability of higher-order multidecker inverse sandwiches arises from the strong coupling between the ground and the low lying charge transfer excited states. The rather strong enhancement of second-hyperpolarizability on increasing size of the beryllium-multidecker inverse sandwiches may provide a new route to design efficient nonlinear optical materials.