The {\em Fibonacci cube} of dimension n, denoted as Γ_n, is the
subgraph of n-cube Q_n induced by vertices with no consecutive 1's. We
study the maximum number of disjoint subgraphs in Γ_n isomorphic to
Q_k, and denote this number by q_k(n). We prove several recursive results
for q_k(n), in particular we prove that q_k(n)=q_k−1(n−2)+q_k(n−3). We also prove a closed formula in which q_k(n) is given in
terms of Fibonacci numbers, and finally we give the generating function for the
sequence {q_k(n)}_n=0∞