A Fibonacci string of order n is a binary string of length n with no two consecutive ones. The Fibonacci cube Γ 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⩾i, the ith extended Fibonacci cube is the vertex induced subgraph of Q n for which V(Γ n i )=V n i is defined recursively byVn+2i=0Vn+1i+10Vni,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. A proper edge colouring of a simple graph G is called strong if it is vertex distinguishing. The observability of G, denoted by obs(G), is the minimum number of colours required for a strong edge colouring of G. In this study we prove that obs(Γ n i )=n+1 when i=1 and 2, and obtain bounds on obs(Γ n i ) for i⩾3 which are sharp in some cases. We also obtain bounds on the value of obs(G×Q n ), n⩾2, for a graph G containing at most one isolated vertex and no isolated edge.