DOI: https://doi.org/10.36347/sjpms.2026.v13i06.001

Pages: 228-240

The problem of “n-multiplying a cube” consists of constructing, by means of a straightedge and compass within the framework of Euclidean geometry, a cube whose volume is exactly n times that of a given cube, where n is a positive integer. This work presents a generalisation of the author’s previously published solutions to the classical problems of “Doubling a Cube” and “Tripling a Cube.” While the classical Greek problems squaring the circle, trisecting an angle, and doubling the cube have been studied extensively throughout the history of mathematics, the more general problem of constructing a cube with volume exactly n times that of a given cube has not appeared in the traditional canon of Euclidean construction problems. Motivated by recent developments concerning the exact construction for doubling a cube and tripling a cube, this paper formulates and investigates a systematic method for the general case. In this article, we present an exact construction-based approach for enlarging a cube by an arbitrary integer factor n, using only the classical Euclidean tools of straightedge and compass. The method is derived from elementary geometric principles and extends naturally from the constructions established in the author’s earlier works on cube duplication and triplication. Although the underlying principles are elementary, the complete development of the method requires a nontrivial sequence of geometric constructions. The results establish a novel framework for constructing a cube whose volume is precisely n times that of a given cube. This framework, referred to as the “n-multiplying a cube” method, provides a systematic and reproducible procedure for exact Euclidean construction without recourse to transcendental quantities or numerical approximation. This work contributes a new perspective to classical geometric construction theory and proposes an extension of constructability within Euclidean geometry through a unified method for volume integered enlargemen