Space Division Multiplexing (SDM) based Elastic Optical Networks (EONs) (SDM-b-EONs) have been envisioned as a solution to both, the required upgradation of the single-mode fiber’s network capacity which is constrained by the non-linear Shannon’s limit and the capacity provisioning which will be necessitated by future diverse Internet traffic. The current SDM-b-EON designs are based on the use of Multiple Fibers (MF) technology; however, recently the Multiple Core Fiber (MCF) technology has gained momentum after laboratory experiments conducted on the MCF models established much lower inter-core crosstalk values. In the current work, we focus on the design of a MCF enabled SDM-b-EON for which, we formulate an Integer Linear Programming (ILP) model and then propose a heuristic algorithm to obtain the solutions for large sized networks in reasonable execution times. We then proceed to the performance comparison of the MCF and the MF enabled SDM-b-EON under the consideration of realistic parameters and network topologies which are characterized by different node(s) numbers and link distances. The obtained results demonstrate that the performance of the MCF enabled SDM-b-EON is very close to that of a MF enabled SDM-b-EON which implies that the network operators can benefit by utilizing the existing components for the MCFs rather than incurring any extra expense to provision the same traffic amount.