Let [ ] be a commutative ring with unity, [ ] be the set of all ideals of [ ] and [ ] be a subset of [ ]. Cayley sum graph of ideals of [ ], denoted by [ ], is a simple undirected graph with vertex set [ ] and two distinct vertices [ ] and [ ] are adjacent ([ ]), whenever [ ] or [ ], for some ideal [ ] in [ ]. In this paper, we determine the girth, chromatic number, clique number, perfect code, and perfectness of the Cayley sum graphs [ ] and [ ] (where [ ] denotes the set of all nonzero maximal ideals of [ ]). Finally, we classify the family of rings whose Cayley sum graphs are split, co-graph, threshold, chordal and claw-free.