The geometrical and electronic structures of the Si(8)(2-) dianion and isovalent silicon clusters doped by main second-row elements including Li@Si(8)(-), Be@Si(8), B@Si(8)(+), C@Si(8)(2+), N@Si(8)(3+), and O@Si(8)(4+), are investigated using quantum chemical methods. The analyses of phenomenological shell model (PSM) combined with partial electron localizability indicators (pELI-D) rationalize the existence of cubic silicon clusters. A cubic cluster can be formed, in the cases of Be@Si(8), B@Si(8)(+), and C@Si(8)(2+), when three conditions are satisfied, namely, a full occupancy of electronic shells (34 electrons), a presence of positive charge at the center, and a type of spherical aromaticity. A chemical bonding picture for the cubic cage of the doped silicon clusters is illustrated. Each Si atom has four lobes of sp(3) hybridization in which three lobes make three covalent sigma bonds with other Si atoms, and the fourth lobe makes a chemical bond with the dopant. The eight delocalized electrons distributed on the fourth lobes describing the bonding between dopant and Si cage follow the Hirsch rule. We demonstrate that a way of applying electron counting rule is to take into account delocalized electrons on the shell orbitals with N > 1 (2S and 2P shell orbitals).