Two-tier 360° video streaming provides a robust solution for handling inaccurate viewport prediction and varying network conditions. Within this paradigm, the client employs a dual-buffer mechanism consisting of a long buffer for panoramic basic-quality segments and a short buffer for high-quality tiles. However, designing an efficient edge caching strategy for two-tier 360° videos is non-trivial. First, as basic-quality segments and high-quality tiles possess different delivery deadlines as well as content popularity, ignoring these discrepancies may result in inefficient edge caching. Second, accurately predicting the popularity of 360° videos at a fine granularity of video segments and tiles remains a challenge. To address these issues, we present DeCa360, a deadline-aware edge caching framework for 360° videos. Specifically, we introduce a lightweight runtime cache partitioning approach to achieve a careful balance between improving the cache hit ratio and guaranteeing more on-time delivery of objects. Moreover, we design a content popularity prediction method for two-tier 360° videos that combines a learning-based prediction model with domain knowledge of video streaming, leading to improved prediction accuracy and efficient cache replacement. Extensive experimental evaluations demonstrate that DeCa360 outperforms all baseline algorithms in terms of byte-hit ratio and on-time delivery ratio, making it a promising approach for efficient edge caching of 360° videos.