The Fibonacci cube Ξnβ is the subgraph of the hypercube induced by the
binary strings that contain no two consecutive 1's. The Lucas cube Ξnβ
is obtained from Ξnβ by removing vertices that start and end with 1. We
characterize maximal induced hypercubes in Ξnβ and Ξnβ and
deduce for any pβ€n the number of maximal p-dimensional hypercubes in
these graphs