Three-dimensional porous carbon materials based on supercubane structure are modeled through first principles based density functional theory calculations. The basic supercubane structure is expanded through the insertion of acetylinic and diacetylinic units between both inter- and intracubane C-C bonds leading to more variety of porous carbon materials. The supercubane is found to be an insulator with an indirect band gap of 5.26 eV and the gap is found to decrease on introducing the acetylinic linking groups between the intercubane C-C bonds. The completely carbomerized supercubane structures are also found to be insulators. We have also calculated the phonon dispersion and the variation in free energy with increasing temperature to verify the stability of the materials considered. The calculated free energy profiles are compared with some of the previously studied carbon allotropes to show the possible thermodynamic stability of these 3D carbon systems. The complex frequency-dependent dielectric constant has been calculated for all the designed structures to study the optical properties such as absorption spectra and energy-loss spectra. As these designed structures are associated with high porosity and reactive carbon sites, we have investigated their hydrogen adsorption properties and it is observed that the expanded supercubanes can adsorb hydrogen with a gravimetric density of ∼2.0 wt %.