Federations among sets of Cloud Providers (CPs), whereby a set of CPs agree to mutually use their own resources to run the VMs of other CPs, are considered a promising solution to the problem of reducing the energy cost. In this paper, we address the problem of federation formation for a set of CPs, whose solution is necessary to exploit the potential of cloud federations for the reduction of the energy bill. We devise a distributed algorithm, based on cooperative game theory, that allows a set of CPs to cooperatively set up their federations in such a way that their individual profit is increased with respect to the case in which they work in isolation, and we show that, by using our algorithm and the proposed CPs' utility function, they are able to self-organize into Nash-stable federations and, by means of iterated executions, to adapt themselves to environmental changes. Numerical results are presented to demonstrate the effectiveness of the proposed algorithm.