A unified recursive method is proposed for constructing magic hypercubes in d-dimensional space for any order n ≥ nbase (nbase = 3 for d = 2 and nbase = 5 for d ≥ 3). The elements form an arbitrary arithmetic progression with first term a ∈ ℝ and common difference g ∈ ℝ \ 0. The distinctive feature of the method is complete fractal nesting: every sub-hypercube aligned with the recursive division grid at any hierarchy level is itself a magic construction. The method is universal, conceptually transparent, mathematically rigorous, and computationally efficient even for large n and high dimensions.
Khusein Ismailovich Khamchiev (Tue,) studied this question.