Based on the density functional theory for exchange-correlation potential, fluorocarbon molecular cages are investigated as building blocks of hyperhalogens. By utilizing C8 F7 as a ligand, a series of hyperhalogen anions, that is, M(C8 F7 )2 (-) (M=Li, Na, and K) and M(C8 F7 )3 (-) (M=Be, Mg, and Ca), are modeled. Calculations show that all the C8 F7 moieties preserve their geometric and electronic integrity in these anions. These anionic molecules possess larger vertical electron detachment energies (5.11-6.45 eV) than that of C8 F7 (-) , verifying their hyperhalogen nature. Moreover, it is also revealed that using larger fluorinated cage C10 F9 as ligands can bring about hyperhalogen anions with larger vertical electron detachment energies. The stability of these studied anions is determined by their large HOMO-LUMO gaps and positive dissociation energies of predetermined possible fragmentation pathways. It is hoped this study will provide an approach for the construction of new types of hyperhalogens and stimulate more research in superatom chemistry.