User recursive functions in Maxima

We consider the problem of dividing a rectangular parallelepiped on finite number of disjoint cubes for some greedy algorithms. The formulated problems are solved by a series of block-functions with direct and indirect (mutual) recursion, written in the programming language of the free Maxima software system. All constructed functions are checked by control calculations. Note that it is impossible to divide a rectangular parallelepiped into pairs of different cubes.
The programming language of system Maxima is used for the following reasons. Statements of the problems solved in this article are quite clear to both the student of secondary school and student of higher education institution. They are also familiar with recursion. So it is only a matter of choosing a programming language for the implementation of the proposed algorithms. And here the language of the Maxima system is quite appropriate. The fact is that in recent years, schools and universities for many reasons, from the many mathematical packages are forced to choose to use freely distributed software. The leaders among such packages are cross-platform Maxima and GeoGebra systems. Therefore, the talk about the features of creating user-defined recursive functions in the Maxima programming language is timely and useful.