A cubic set is one of the most recently introduced algebraic structures consisting of a non-empty set together with an interval-valued fuzzy set and an ordinary fuzzy set. The new notion of cubic soft matrix, order relation among cubic soft matrices and union and the intersection of cubic soft matrices are introduced. Two new types of cubic soft matrices, namely internal cubic soft matrices and external cubic soft matrices are defined and their related properties are discussed. The new notions of P-order (R-order) on internal and external cubic soft matrices are introduced. The union and...