Calculate number of small cubes making up large cube given number in outermost layer I have a large cube made up of many smaller cubes. Each face of the cube is identical, and all of the smaller cubes are identical. I need to calculate the number of small cubes that make up the large cube. Just to make it clear, the cube is _solid_ (made up of little cubes all the way through). The only value I have to work this out from is the number of small cubes that make up the outermost layer. This number is $100,614,152$. What is the simplest way to calculate the total number of small cubes making up the large cube?

Let the big cube be of dimension $(x+2)$ (made up of $(x+2)^3$ smaller cubes). Then $(x+2)^3-x^3=100,614,152$. This reduces to a quadratic equation which you can solve.