Based on first-principle FLAPW-GGA calculations, we have investigated structural and electronic properties of the recently synthesized tetragonal (space group P4/nmm) nickel-based pnictide oxide superconductors: 3.3K (Ni2P2)(Sr4Sc2O6) and 2.7K (Ni2As2)(Sr4Sc2O6). Optimized structural data, electronic bands, total and partial densities of states, and Fermi surface topology have been obtained and discussed in comparison with available experiments and with their Fe-based (Fe2P2)(Sr4Sc2O6) and (Fe2As2)(Sr4Sc2O6) analogs.