The deployment of low earth orbit (LEO) satellites with terrestrial networks can potentially increase the efficiency and reduce the cost of relaying content from a data center to a set of edge caches hosted by 6G and beyond enabled macro base stations. In this work, the characteristics of the communication system and the mobility of LEO satellites are thoroughly discussed to describe the channel characteristics of LEO satellites, in terms of their frequency bands, latency, Doppler shifts, fading effects, and satellite access. Three different scenarios are proposed for the relay of data from data centers to edge caches via LEO satellites, which are the "Immediate Forward", "Relay and Forward", and "Store and Forward" scenarios. A comparative problem formulation is utilized to obtain numerical results from simulations to demonstrate the effectiveness and validity as well as the trade-offs of the proposed system model. The simulation results indicate that the integration of LEO satellites in edge caching for 6G and beyond networks decreased the required transmission power for relaying the data from the data center to the edge caches. Future research directions based on the proposed model are discussed.