Abstract: Let n be any positive integer,and S(n) be the cubic complements of n.The main purpose of this paper is to study the asymptotic of sum from (n≤x) (n/(S(n)))k (k≥1).And by using the elementary methods,it intends to give two sharper asymptotic formulas,and thus extends the related conclusious.

Key words: cubic complement, reciprocal, mean value, asymptotic formula