This article investigates the problem of distributed cooperative energy management of multiple energy bodies with the consideration of both the optimal energy generation/consumption of each participant within single energy body and the optimal energy distribution on the interconnected lines between any pair of energy bodies. First, we define the physical and communication structure of the system formed by many energy bodies, each of which is viewed as a multienergy prosumer. Then, a distributed energy management model is proposed to achieve not only maximum profits of overall energy generation and consumption, but also minimum cost of energy delivery. To address this issue, a distributed double-Newton descent (DDND) algorithm is proposed, which possesses two advantages. On the one hand, by employing second-order information, the concept of Newton descent is embedded into the implementation of the proposed algorithm, resulting in faster convergence speed. On the other hand, the proposed algorithm performs in a fully distributed fashion. As a consequence, each participant can locally obtain its optimal operation as well as the global energy market clearing prices; meanwhile, each energy router can locally obtain the optimal exchanged energy with its neighbor energy routers. Moreover, we prove that the proposed DDND algorithm can asymptotically converge to the global optimal point. As a result, the correctness of the DDND algorithm can be guaranteed in theory. Finally, simulation results validate the effectiveness of the proposed algorithm.