A group which act properly on a CAT(0) cubical complex, while not necessarily amenable, satisfies several weak forms of amenability: such a group is a-T-menable, weakly amenable and K-theoretically amenable. In the talk, based on joint work with J. Brodzki and N. Higson, I will describe a proof of K-amenability which finds its roots in earlier work of P. Julg and A. Valette on groups acting on trees. I will focus on the geometric constructions involved, and will keep the analytic complications to a minimum.