In smart factory operations, equipment inspection is a critical process for ensuring production safety and efficiency. Owing to their flexibility, safety, and efficiency, Unmanned Aerial Vehicles (UAVs) have been widely adopted in smart factory inspection systems. However, constrained by limited computational power and battery capacity, data collected by UAVs can be offloaded to servers for collaborative computation. Meanwhile, inspection tasks typically exhibit strong dependencies, heterogeneity, and periodicity, which complicates offloading decisions and compromises real-time performance. To address these challenges, we establish a three-layer computational offloading architecture, a cloud-edge-UAV collaborative inspection system, and propose a Cache-Assisted Task Offloading (CATO) strategy aimed at minimizing system delay. First, a multi-metric task prioritization mechanism optimizes the execution order of subtasks. Second, an edge cache placement strategy reduces redundant computation for periodic tasks. Further, a preference-based task-server bi-directional matching model incorporating a stable matching algorithm ensures efficient offloading. Finally, we implement dynamic co-optimization of caching and offloading via iterative updates to further enhance system performance. Simulation results show that CATO reduces system delay by up to 20.0 \(\%\) compared to NoCache strategy.