Space-Ground Integrated Networks (SGINs) hold the potential to enable seamless and high-quality global coverage in an economically viable manner. However, the limited bandwidth and relatively long delay of satellite-ground links pose significant challenges in meeting the increasing demands driven by surging traffic. To address this issue, we propose a three-tier cooperative caching architecture incorporating base stations (BSs), satellites, and a content server, which aims to reduce the average content retrieval delay through cooperative caching between BSs and satellites. The joint optimization problem among them is both challenging to solve and non-scalable due to its exponentially increasing computational complexity. Meanwhile, the geographic characteristics of requests are overlooked in existing work. As a consequence, we propose a novel block partitioning algorithm based on the popularity similarity across areas to facilitate cooperative caching, which reduces the computational complexity, and ensures the scalability and the effectiveness of cooperative caching. Based on the partitioned blocks, the optimization problem is decomposed into two subproblems: intra-block cooperative optimization among BSs and inter-block cooperative optimization among satellites, effectively catering to the characteristics of wide-area coverage in SGINs. For the subproblems with finite dimensions, Semidefinite Relaxation (SDR) based intra-block and inter-block cooperative caching approaches are proposed to obtain the optimal cooperative caching strategies. Extensive simulations demonstrate that, compared to directly solving the original problem, the proposed algorithm reduces the solving time from exponential to linear growth. Moreover, our algorithm outperforms existing schemes by reducing 13% average retrieval delay and improving 12% overall cache hit rate.