Some Generalized Formula For Sums of Cube

The study of integer representations as a sum of powers is still a very long standing problem.Inthis work, the study of integer representation as a sum of cube is introduced and investigated fornon-zero distinct integer solution.Leta1, a2, a3,···, ananddbe any positive integers such thatan−an−1=an−1−an−2=···=a2−a1=d.This study formulates some general resultsfor sums ofncube.In particular, this research introduces and develops the diophantine equationI= (a1+a2+a3+···+an)L=a31+a32+a33+···+a3nfor some integerL. The method involves decomposingintegerIinto sums ofncube and determination of general representation of integerLusing case by case basis.