Carbon nanocage structures such as fullerene, nanotubes, nanocapsules, nanopolyhedra, cones, cubes, and onions have been reported since the discovery of C60, and they offer tremendous promise for investigating materials of low dimensions in an isolated environment. Boron Nitride (BN) nanomaterials such a: nanotubes, nanocapsules, nanoparticles, and clusters have been described in several studies and are predicted to be useful as electronic devices, high heat-resistance semiconductors, nanocables, insulator lubricants, and gas storage materials. The interaction, and electronic of octahedral B12N12 nanocage cluster covalently modified from the attachment of alkyl and aryl radicals were analyzed using Density Functional Theory calculations. The work discusses for the first time to our knowledge the complete investigation of the impact of the grafted aryl and alkyl groups on the electronic, bang gap, and density of states on the B12N12. Furthermore, this is the first complete description of these radicals attaching to a surface of B12N12 nanocage cluster.