Capitalizing on the talent of self-attention in capturing non-local features, Transformer architectures have exhibited remarkable performance in single hyperspectral image restoration. For hyperspectral images, each pixel is located in the hyperspectral image cubes with a large spectral dimension and two spatial dimensions. Although uni-dimensional self-attention, like channel self-attention or spatial self-attention, builds long-range dependencies in spectral or spatial dimensions, they lack more comprehensive interactions across dimensions. To tackle the above drawback, we propose a VolFormer, a volumetric self-attention embedded Transformer network for single hyperspectral image restoration. Specifically, we propose volumetric self-attention (VolSA), which extends the interaction from 2D flat to 3D cube. VolSA can simultaneously model token interaction in the 3D cube, mining the potential correlations between the hyperspectral image cube. An attention decomposition form is proposed to reduce the computational burden of modeling volumetric information. In practical terms, VolSA adapts double similarity matrixes in spatial and channel dimensions to implicitly model 3D context information while transforming the complexity from cubic to quadratic. Additionally, we introduce the explicit spectral location prior to enhance the proposed self-attention. This property allows the target token to perceive global spectral information while simultaneously assigning different levels of attention to tokens at varying wavelength bands. Extensive experiments demonstrate that VolFormer achieves record-high performance on hyperspectral image super-resolution, denoise and classification benchmarks. Particularly, VolSA is portable and achieves inspiring results in hyperspectral classification. The source code is available in the supplementary material.