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 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. 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.