In this paper, mystic miscellaneous algebraic properties of the set of 9 × 9 Composite (Nested) Loube̠re̠Magic Squares are vividly visualized. And, verbatim virtuoso of algebraic properties of the 3 × 3 Loube̠re̠Magic Squares viz: Eigen group, Magic Sum group and Centre Pieces group viewed the algebraic properties of its 9 × 9 Composite. It is also showcased that both the 2 sets equipped with the matrix binary operation of addition form infinite additive abelian groups.