Let i be a positive integer. A complete bipartite graph K1,i is called an i-star, denoted by Si. An {S2,S3}-packing of a graph G is a collection of vertex-disjoint subgraphs of G in which each subgraph is a 2-star or a 3-star. The maximum {S2,S3}-packing problem is to find an {S2,S3}-packing of a given graph containing the maximum number of vertices. The perfect {S2,S3}-packing problem is to answer whether there is an {S2,S3}-packing containing all vertices of the given graph. The perfect {S2,S3}-packing problem is NP-complete in general graphs. In this paper, we prove that the perfect {S2,S3}-packing problem remains NP-complete in cubic graphs and that every simple cubic graph has an {S2,S3}-packing covering at least six-sevenths of its vertices. Our proof infers a quadratic-time algorithm for finding such an {S2,S3}-packing of a simple cubic graph.