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The next generation multibeam satellites open up a new way to design satellite communication channels with the full flexibility in bandwidth, transmit power and beam coverage management. In this paper, we exploit the flexible multibeam satellite capabilities and the geographical distribution of users to improve the performance of satellite-assisted edge caching systems. Our aim is to jointly optimize the bandwidth allocation in multibeam and caching decisions at the edge nodes to address two important problems: i) cache feeding time minimization and ii) cache hits maximization. To tackle the non-convexity of the joint optimization problem, we transform the original problem into a difference-of-convex (DC) form, which is then solved by the proposed iterative algorithm whose convergence to at least a local optimum is theoretically guaranteed. Furthermore, the effectiveness of the proposed design is evaluated under the realistic beams coverage of the satellite SES-14 and Movielens data set. Numerical results show that our proposed joint design can reduce the caching feeding time by 50\% and increase the cache hit ratio (CHR) by 10\% to 20\% compared to existing solutions. Furthermore, we examine the impact of multispot beam and multicarrier wide-beam on the joint design and discuss potential research directions.