Energy hub integrates various energy conversion and storage technologies, which can yield complementarity among multiple energy and provide consumers with stable energy services, such as electricity, heating, and cooling. This enables energy hub to be an ideal energy system design for smart and green buildings. This paper proposes a distributed auction mechanism for multi-energy scheduling of an energy hub that serves numbers of building energy users. In the auction, users first submit their demand data to the hub manager. Then, the hub manager allocates energy to users via optimization of energy scheduling based on the users' data. The auction mechanism is designed to be incentive compatible, meaning that users are incentivized to truthfully submit their demand data. Next, to mitigate the computational burden of the hub manager, a distributed implementation of the auction is developed, in which an algorithm based on alternating direction method of multipliers (ADMM) is adopted to offload auction computation onto the users. Distributed computation offloading may bring in new chances for users to manipulate the auction outcome since the users participate part of the auction computation. It is proven that the proposed distributed auction mechanism can achieve incentive compatibility in a Nash equilibrium, which indicates that rational users will faithfully report demand data and complete the assigned computation as well. Finally, simulation results based on a household energy consumption dataset are presented to evaluate the energy scheduling performance and to verify the incentive compatibility of the auction mechanism.