In multi-access edge computing (MEC) systems, there are multiple local cache servers caching contents to satisfy the users' requests, instead of letting the users download via the remote cloud server. In this paper, a multi-cell content scheduling problem (MCSP) in MEC systems is considered. Taking into account jointly the freshness of the cached contents and the traffic data costs, we study how to schedule content updates along time in a multi-cell setting. Different from single-cell scenarios, a user may have multiple candidate local cache servers, and thus the caching decisions in all cells must be jointly optimized. We first prove that MCSP is NP-hard, then we formulate MCSP using integer linear programming, by which the optimal scheduling can be obtained for small-scale instances. For problem solving of large scenarios, via a mathematical reformulation, we derive a scalable optimization algorithm based on repeated column generation. Our performance evaluation shows the effectiveness of the proposed algorithm in comparison to an off-the-shelf commercial solver and a popularity-based caching.