Generating high-quality 360° panoramic videos from perspective input is one of the crucial applications for virtual reality (VR), whereby high-resolution videos are especially important for immersive experience. Existing methods are constrained by computational limitations of vanilla diffusion models, only supporting $\leq$ 1K resolution native generation and relying on suboptimal post super-resolution to increase resolution. We introduce CubeComposer, a novel spatio-temporal autoregressive diffusion model that natively generates 4K-resolution 360° videos. By decomposing videos into cubemap representations with six faces, CubeComposer autoregressively synthesizes content in a well-planned spatio-temporal order, reducing memory demands while enabling high-resolution output. Specifically, to address challenges in multi-dimensional autoregression, we propose: (1) a spatio-temporal autoregressive strategy that orchestrates 360° video generation across cube faces and time windows for coherent synthesis; (2) a cube face context management mechanism, equipped with a sparse context attention design to improve efficiency; and (3) continuity-aware techniques, including cube-aware positional encoding, padding, and blending to eliminate boundary seams. Extensive experiments on benchmark datasets demonstrate that CubeComposer outperforms state-of-the-art methods in native resolution and visual quality, supporting practical VR application scenarios. Project page: https://lg-li.github.io/project/cubecomposer