This paper examines the integration of vector coded caching (VCC) into multi-beam satellite communications (SATCOM) systems and demonstrates that even limited receiver-side caching can substantially enhance spectral efficiency. By leveraging cached content to suppress interference, VCC enables the concurrent transmission of multiple precoded signal vectors that would otherwise require separate transmission resources. This leads to a multiplicative improvement in resource utilization in SATCOM. To characterize this performance, we model the satellite-to-ground channel using Rician-shadowed fading and after incorporating practical considerations such as matched-filter precoding, channel state information (CSI) acquisition overhead as well as CSI imperfections at the transmitter, we here derive closed-form expressions for the average sum rate and spectral efficiency gain of VCC in SATCOM. Our analysis, tightly validated through numerical simulations, reveals that VCC can yield spectral efficiency gains of 300% to 550% over traditional multi-user MISO SATCOM with the same resources. These gains -- which have nothing to do with multicasting, prefetching gains nor file popularity -- highlight VCC as a pure physical-layer solution for future high-throughput SATCOM systems, significantly narrowing the performance gap between satellite and wired networks.