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We systematically investigate the electronic structure, magnetism and high-temperature superconductivity (SC) in the multi-layer octagraphene and octagraphite (bulk octagraphene). A tight binding model is used to fit the electronic structures of single-layer, multi-layer octagraphenes and octagraphite. We find that the multi-layer octagraphene and octagraphite follow a simple A-A stacking structure from the energy analysis. The van der Waals interaction induces $t_{\perp}\approx0.25$ eV and the hopping integrals within each layers changes little when the layer number $n$ increases. There is a well Fermi-surface nesting with nesting vector $\mathbf{Q}=(π,π)$ for the single-layer octagraphene at half-filling, which can induce a 2D Néel antiferromagnetic order. With increasing the layer number $n\rightarrow\infty$, the Fermi-surface nesting transforms to 3D with nesting vector $\mathbf{Q}=(π,π,π)$ and shows the system has a 3D Néel antiferromagnetic order. Upon doping, the multi-layer octagraphene and octagraphite can enter a high-temperature $s^{\pm}$ SC driven by spin fluctuation. We evaluate the superconducting transition temperature $T_c$ by using the random-phase approximation (RPA), which yields a high $T_c$ even if the layer number $n\geq$ 3. Our study shows that the multi-layer octagraphene and octagraphite are promising candidates for realizing the high-temperature SC.