Summary: ``A cycle containing a shortest path between two vertices $u$ and $v$ in a graph $G$ is called a $(u, v)$-geodesic cycle. A connected graph $G$ is geodesic 2-bipancyclic, if every pair of vertices $u$, $v$ of it is contained in a $(u, v)$-geodesic cycle of length $l$ for each even integer $l$ satisfying $2d + 2\leq l\leq |V (G)|$, where $d$ is the distance between $u$ and $v$. In this paper, we prove that the Cartesian product of two geodesic hamiltonian graphs is a geodesic 2-bipancyclic graph. As a consequence, we show that for $n\geq 2$ every $n$-dimensional torus is a geodesic 2-bipancyclic graph.''