In cloud computing, a private (secondary) cloud can: 1) outsource workload to public (primary) clouds via vertical federation or 2) share resources with other secondary clouds through horizontal federation to enhance its service quality. While there have been attempts to establish a joint vertical and horizontal cloud federation (VHCF), little is known regarding the economic aspects (e.g., what stable cooperation pattern will form, will it improve efficiency) of such a complex cloud network, where secondary clouds are self-interested. To fill the gap, we analyze the interrelated workload factoring and federation formation among secondary clouds, while providing scalable algorithms to assist them to optimally select partners and outsource workload. We use a game theoretic approach to model the federation formation of clouds as a coalition game with externalities. We adopt a pessimistic core to characterize the cooperation stability and formulate its computation as a bilevel optimization problem. The properties of the problem are explored and efficient algorithms are developed to solve it. Experimental results show that the two common practices (no-cooperation and all-in-one federation) are not always stable. The results also show that compared with the two common practices, secondary clouds can decrease service delay penalty by around 11% with the proposed VHCF network.