Supercomputers of the 21st century are massively parallel systems: they embody hundreds of thousands of compute nodes. Hence, node interconnection is critical to achieve high performances – this is the role of the interconnection network – just as routing algorithms are. Although routing obviously involves paths inside the interconnection network, it also relies on cycles to solve issues, like the multicast problem. Because torus-based hierarchical interconnection networks have become popular as interconnect of modern supercomputers (e.g. the Fujitsu K and Fugaku machines), we focus in this paper on the torus-connected cycles (TCC) topology. In this paper, we formally discuss pancyclicity in the case of a TCC network: we give a constructive proof that shows that when it is two-dimensional and of arity three, a TCC is bipancyclic and vertex bipancyclic, and for greater arities, we propose an algorithm that realises cycle embeddings as large as the network order. The corresponding algorithm for finding such cycles is then evaluated, both theoretically and empirically. The obtained results show that the proposed algorithms are of polynomial order of the number of nodes, whereas it is known that solving the pancyclicity problem for any graph is an NP-hard problem.