This study addresses the challenges of joint computation offloading and resource allocation in low-earth orbit (LEO) satellite networks. To effectively manage the computational demands of LEO satellites, we propose a collaborative framework that allows each LEO satellite to offload tasks either to high-earth orbit (GEO) satellites or to multi-access edge computing (MEC) servers on the ground. Our goal is to jointly optimize the offloading ratio, computational frequency, transmission power, and bandwidth utilization of the LEO satellites, aiming to minimize the overall energy consumption while adhering to latency requirements. We formulate this challenge as a non-convex optimization problem and introduce an energy-efficient layered optimization approach to address it with reduced complexity. This involves breaking down the original problem into several manageable subproblems, which are solved sequentially to achieve a suboptimal solution. The simulation results confirm the effectiveness of our method, demonstrating its advantages over existing benchmark algorithms.