To create your own model to print you begin by using one of the CAD (computer aided design) software packages. There are several that you can choose from. One of the most popular is Tinkercad, which was purchased and has become part of the Autodesk programs. You need to create an account to use the software, but it is free. Another popular tool, also created by Autodesk is 123D Design. Regardless of which tool you choose, Autodesk has a terrific site that has lesson plans and ideas with videos and steps on how to create different projects. Check out some of them here. This page will provide instructions for creating your own model in 123D, because it has both an online downloadable and iPad app versions.
The idea of this block puzzle is that you have pieces that can be placed together to complete a cube. The cubes consist of 27 10X10 cm squares, so 27 blocks in total. To begin the project you can download a free copy of 123D Design from http://www.123dapp.com/design