Dominance is a fundamental concept in graph theory. Motivated by applications in facility location problems, we study colorful k-rainbow domination. Given a graph \(G=(V, E)\) and a set of k colors, we consider a function f that assigns a subset of colors to each vertex. This function is called the colorful k-rainbow dominating function of G if two conditions hold. First, for each vertex v, its closed neighborhood N[v] contains all k different colors. Second, each vertex v gets a non-empty color set. The weight of f is the total number of colors assigned. The goal of the colorful k-rainbow domination problem is to find a colorful k-rainbow dominating function with the smallest weight, called the colorful k-rainbow domination number. Colorful 3-rainbow domination is NP-complete in general graphs, but solvable in linear time for trees. We give linear time algorithms that compute an optimal colorful 3-rainbow domination function if an input graph is a block or a cactus graph. Furthermore, we show that the corresponding problem remains NP-complete if we restrict the input graph to the class of maximum degree 3 graphs.