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n*n*n
The definition of a perfect cube is the cube of a number n is its third power. This is formula that is used for finding volume.
The number 784 is not a perfect cube. A perfect cube is defined as a number that can be expressed as the cube of an integer (i.e., (n^3) for some integer (n)). The cube root of 784 is approximately 9.24, which is not an integer, indicating that 784 cannot be represented as a whole number cubed.
Let n > 1 for an n x n x n cube for the purpose of decomposing the n x n x n cube into unit cubes (1 x 1 x 1). For the above scenario we see that decomposing an n x n x n cube into unit cubes can be thought of dividing an n x n x n cube into unit cubes. When n = 2 we get 8 unit cubes after decomposing. When n = 3 we get 27 unit cubes after decomposing.If necessary to further your understanding I would suggest drawing a picture of a 2 x 2 x 2 cube then divide each of the six-faces by 2 both horizontally and vertically. Then draw a 3 x 3 x 3 cube and then divide each of its six-faces by 3 both horizontally and vertically. Then count the number of unit cubes for both drawings. Again, when n = 2 you should count 8 unit cubes and when n = 3 you should count 27 unit cubes.
To find a number that is a perfect cube, take an integer, mulitply it by itself and again. The answer is a perfect cube. Thus n * n * n To find a perfect cube as a 3 dimensional object is not possible. It is a concept that can exist only in your imagination. Any physical representation is bound to have microscopic (or smaller) flaws - certainly at the sub-atomic level.