A magie square (a square array containing natural numbers 1,2, ... , n2 such that the sum of the numbers along every row, column and diagonal is the same) has fascinated people for centuries. In 1686, the Polish rnathematician Adamas Kochansky extended magic squares to three dimensions. An additive magic cube is a natural generalization of a magic square.
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An additive magic cube is a cubical array containing different natural numbers such that the sum of the numbers along every row and every diagonal is the same. A multiplicative magic cube is cubical array containing mutually different natural numbers such that the product of the numbers along each row and diagonal is the same. In this paper we give several ways to construct additive and multiplicative magic cubes.
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