We use techniques of the theory of algorithms of differentiation of posets and P-partitions to describe identities of some one-dimensional compositions involving polygonal and cubic numbers. We also describe with these techniques numbers which can be written as a sum of three square of numbers of a given shape or sequences of numbers which can be written as sums of three, four or five cubic numbers.

algorithm of differentiation, composition, cubic number, lattice path, linear extension, P-partition, polygonal number, poset, representation of posets.