The k-dimensional data center network with n-port switches, denoted by Dk,n, has been proposed for data centers as a server centric network structure. Wang et al. had proved that Dk,n is Hamiltonian-connected for k≥0 and n≥2 except for (k,n)=(1,2). In this paper, we prove that for any edge (u,v) in a complete subgraph Kn of Dk,n, there is a cycle of every length from 3 to |V(Dk,n)| passing through the edge (u,v) in Dk,n for n≥5. As corollaries, we obtained that Dk,n is vertex-pancyclic and pancyclic.