BCube, as a popular server-centric data center network (DCN), offers significant advantages in low latency, load balancing, and high bandwidth. The many-to-many paired $m$-disjoint path cover ($m$-DPC), a generalization of Hamiltonian paths, enhances message transmission efficiency by constructing disjoint paths that connect $m$ source-destination pairs while covering all the nodes. However, with the continuous expansion of DCNs, link and service failures have grown increasingly common, necessitating robust fault-tolerant algorithms to guarantee reliable communication.This paper mainly investigates the fault-tolerant paired 2-DPC embedding in BCube. We prove that under the partitioned edge fault (PEF) model, BCube retains a paired 2-DPC even when exponentially many edge failures occur.