Summary: A Fibonacci string of order \(n\) is a binary string of length \(n\) with no two consecutive ones. The Fibonacci cube \(\Gamma _n\) is the subgraph of the hypercube \(Q_n\) induced by the set of Fibonacci strings of order \(n\). For positive integers \(i,n\), with \(n \geq i\), the \(i\)th extended Fibonacci cube is the vertex induced subgraph of \(Q_n\) for which \(V(\Gamma _n^i)=V _n^i\) is defined recursively by \(V_{n+2}^i=0V_{n+1}^i + 10V_n^i\), with initial conditions \(V_i^i=B_i\), \(V_{i+1}^i = B_{i+1}\), where \(B_k\) denotes the set of binary strings of length \(k\). In this study, we answer in the affirmative a conjecture of J. Wu that the sequences \(\{| V_n^i | \}_{n=1+2}^{\infty }\) are pairwise disjoint for all \(i \geq 0\), where \(V_n^0 = V(\Gamma _n)\).