Caching holds the promise of scaling the service capability of next-generation radio access networks (RANs), thereby attracting much recent attention in the era of 6G research. To enable caching, popular content items should be proactively pushed to the user ends (UEs) in the placement phase. In practice, most content placement is only allowed to exploit idle spectrum or timeslot that is not occupied by any on-demand transmissions. In this case, however, the performance analysis and optimizations of practical caching gains remain open. In this paper, we are interested in how pushing, as a secondary service, improves the overall performance in terms of energy efficiency and latency reduction. To this end, we formulate a Markovian queueing model, the caching gains of which are optimized via linear programming (LP) with acceptable computational complexity. Our work demonstrates that the peak traffic load due to burst on-demand transmissions, as primary services, can be effectively offloaded by pushing over idle timeslots, leading to substantially reduced power consumption and queueing delay.