Is there a term to refer to a cube-break-down process? The image shown below illustrate the process to break a cube down into 4 small equal cubes.

Is there a term to refer to this process, something like cube-break-down?



Why would I like to know the term?  

Because I am trying to perform this process by coding, and I am wondering if there existing code base to do this.
What about Division or subdivision?