Keep in mind that a covalent bond is a pair of electrons shared between two atoms. Keep in mind also that Lewis' first ideas about a cube were quickly replaced. The reasons why will be discussed.
In 1902, Lewis wrote down his first, crude ideas on chemical bonding. He visualized the outer shell of an atom as a cube with electrons at each vertex. Inner shells of electrons were smaller cubes inside. He knew that in a stable atom or molecule (except hydrogen) that there must be eight electrons around each atom.
The following diagram is rather famous and is reproduced in many textbooks. It is what Lewis wrote in a memorandum dated March 28, 1902.
He never published the ideas of 1902, but he did use them in his classroom teaching. Lewis did not write a bonding article until 1913 with his most important article appearing early in 1916.
In 1923, Lewis wrote:
"In the year 1902 (while I was attempting to explain to an elementary class in chemistry some of the ideas Involved in the periodic law) becoming interested in the new theory of the electron, and combining this idea with those which are implied in the periodic classification, I formed an idea of the inner structure of the atom which, although it contained certain crudities, I have ever since regarded as epresenting essentially the arrangement of electrons in the atom.
In accordance with the idea of Mendeleef, that hydrogen is the first member of a full period, I erroneously assumed helium to have a shell of eight electrons. Regarding the disposition in the neutral charge which balanced the electrons in the neutral atom, my ideas were very vague; I believe I inclined at that time toward the idea that the positive charge was also made up of discrete particles, the localization of which determined the localization of the electrons.
The main features of this theory of atomic structure are as follows:
(1) The electrons in an atom are arranged in concentric cubes.
(2) A neutral atom of each element contains one more electron than a neutral atom of the element next preceeding.
(3) The cube of 8 electrons is reached in the atoms of the rare gases, and this cube becomes in some sense the kernal about which the larger cube of electrons of the next period is built.
(4) The electrons of an outer incomplete cube may be given to another atom, as in Mg++, or enough electrons may be taken from other atoms to complete the cube, as in Cl¯, thus accounting for "positive and negative valence."
Lewis could account for polar molecules (i.e. ionically bonding substances like NaCl) like this: