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?
Best Answer
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.