The use of dyadic interaction between agents, in combination with homophily (the principle that "likes attract") in the Axelrod model for the study of cultural dissemination, has two important problems: the prediction of monoculture in large societies and an extremely narrow window of noise levels in which diversity with local convergence is obtained. Recently, the inclusion of social influence has proven to overcome them [A. Flache and M. W. Macy, e-print arXiv:0808.2710]. Here, we extend the Axelrod model with social influence interaction for the study of mass media effects through the inclusion of a superagent which acts over the whole system and has non-null overlap with each agent of the society. The dependence with different parameters as the initial social diversity, size effects, mass media strength, and noise is outlined. Our results might be relevant in several socioeconomic contexts and for the study of the emergence of collective behavior in complex social systems.