On Generalized Sums of Six, Seven and Nine Cube

Abstract

Let u1, u2, u3,・・・ un be integers such that un − un−1 = un−1 − un−2 = ・ ・ ・ = a2 − a1 = d. In this article, the study of sums of cube in arithmetic progression is discussed. In particular, the study develops and introduces some generalized results on sums of six, seven and nine cube for any arbitrary integers in arithmetic sequences. The method of study involves analogy grounded on integer decomposition and factorization. The result in this study will prove the existing results on sums of cubes.