This theory was developed in 1902 by Gilbert N. Lewis and published in 1916 in the article "The Atom and the Molecule" and used to account for the phenomenon of valency.
Although the cubical model of the atom was soon abandoned in favor of the quantum mechanical model based on the Schrödinger equation, and is therefore now principally of historical interest, it represented an important step towards the understanding of the chemical bond.
Ionic bonds are formed by the transfer of an electron from one cube to another without sharing an edge (structure A).
Triple bonds could not be accounted for by the cubical atom model, because there is no way of having two cubes share three parallel edges.
Lewis suggested that the electron pairs in atomic bonds have a special attraction, which result in a tetrahedral structure, as in the figure below (the new location of the electrons is represented by the dotted circles in the middle of the thick edges).