In 1977, Solomon L. introduced a zeta function for orders for which all ideals of finite index must be known. This work follows our previous research [Zeta functions of Burnside rings of groups of order p and p2, Comm. Algebra, 37(2009), 1758-1786], where we found the zeta function of the Burnside Ring for cyclic groups of prime order p and p2, respectively. The main objective of this paper is to obtain all ideals of finite index in Bp(Cp3 ) in order to determine ζBp(Cp3 ) (s) the zeta function of the Burnside Ring for a cyclic group of order p3..