Expressing an integer as a sum of cubes of polynomials

Abstract: In this paper we prove that there exist infinitely many integers which can be expressed as a sum of four cubes of polynomials with integer coefficients. We give several identities that express the integers 1 and 2 as a sum of four cubes of polynomials. We also show that every integer can be expressed as a sum of five cubes of polynomials with integer coefficients.