With the development of mobile edge computing (MEC) and blockchain-based federated learning (BCFL), a number of studies suggest deploying BCFL on edge servers. In this case, resource-limited edge servers need to serve both mobile devices for their offloading tasks and the BCFL system for model training and blockchain consensus in a cost-efficient manner without sacrificing the service quality to any side. To address this challenge, this paper proposes a resource allocation scheme for edge servers, aiming to provide the optimal services with the minimum cost. Specifically, we first analyze the energy consumed by the MEC and BCFL tasks, and then use the completion time of each task as the service quality constraint. Then, we model the resource allocation challenge into a multivariate, multi-constraint, and convex optimization problem. To solve the problem in a progressive manner, we design two algorithms based on the alternating direction method of multipliers (ADMM) in both the homogeneous and heterogeneous situations with equal and on-demand resource distribution strategies, respectively. The validity of our proposed algorithms is proved via rigorous theoretical analysis. Through extensive experiments, the convergence and efficiency of our proposed resource allocation schemes are evaluated. To the best of our knowledge, this is the first work to investigate the resource allocation dilemma of edge servers for BCFL in MEC.