To explore stable polynuclear magnetic superhalogens, we perform an unbiased structure search for polynuclear iron-based systems based on pseudohalogen ligand CN using the CALYPSO method in conjunction with density functional theory. The superhalogen properties, magnetic properties, and thermodynamic stabilities of neutral and anionic Fe-2(CN)(5) and Fe-3(CN)(7) clusters are investigated. The results show that both of the clusters have superhalogen properties due to their electron affinities (EAs) and that vertical detachment energies (VDEs) are significantly larger than those of the chlorine element and their ligand CN. The distribution of the extra electron analysis indicates that the extra electron is aggregated mainly into pseudohalogen ligand CN units in Fe-2(CN)(5)(-) and Fe-3(CN)(7)(-) cluster. These features contribute significantly to their high EA and VDE. Besides superhalogen properties, these two anionic clusters carry a large magnetic moment just like the Fe2F5- cluster. Additionally, the thermodynamic stabilities are also discussed by calculating the energy required to fragment the cluster into various smaller stable clusters. It is found that Fe(CN)(2) is the most favorable fragmentation product for anionic Fe-2(CN)(5)(-) and Fe-3(CN)(7)(-) clusters, and both of the anions are less stable against ejection of Fe atoms than Fe(CN)(n-x).