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We present molecular dynamics (MD) simulations of radiation damage in pure Fe nanoparticles (NP) and bimetallic FeCu core-shell nanoparticles (CSNP). The CSNP includes a perfect body centered cubic (bcc) Fe core coated with a face-centered cubic (fcc) Cu shell. Irradiation with Fe Primary Knock-on Atoms (PKA) with energies between 1 and 7 keV leads to point defects, without clustering beyond divacancies and very few slightly larger vacancy clusters, and without interstitial clusters, unlike what happens in bulk at the same PKA energies. The Fe-Cu interface and shell can act as a defect sink, absorbing radiation-induced damage and, therefore, the final number of defects in the Fe core is significantly lower than in the Fe NP. In addition, the Cu shell substantially diminishes the number of sputtered Fe atoms, acting as a barrier for recoil ejection. Structurally, the Cu shell responds to the stress generated by the collision cascade by creating and destroying stacking faults across the shell width, which could also accommodate further irradiation defects. Sputtering yield (Y) is underestimated by BCA, which is also expected since the simulation is for a thin film at normal incidence. We also compare MD defect production to bulk predictions of the analytic Athermal Recombination Corrected Displacements Per Atom (arc-dpa) model. The number of vacancies in the Fe core is only slightly lower than arc-dpa predictions, but the number of interstitials is reduced by about one order of magnitude compared to vacancies, at 5 keV. According to the radiation resistance found for FeCu CSNP in our simulations, this class of nanomaterial could be suitable for developing new radiation resistant coatings, nanostructured components, and shields for use in extreme environments, for instance, in nuclear energy and astrophysical applications.