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We revisit the highly debated mixed-valence compound SmB6, which has been widely studied in both theory and experiment. One outstanding challenge is the difficulty in obtaining accurate theoretical band structures of SmB₆ as the starting point for further theoretical studies. We report new first-principles electronic-structure results, finding a band structure in agreement with experiments, wherein the correct crystal field splitting of f electrons is captured by considering magnetic configurations. Intermediate valency and the right ground state symmetry are also captured in our calculations. The energies for each magnetic ordering are extremely close, indicating that SmB6 exhibits spin fluctuations. Moreover, our results confirm that SmB₆ is a robust Kondo topological insulator due to its strong d and f band hybridization. Our study paves the way for future mean-field theory investigations of electronic and atomic structures, phase diagrams, and band topology of f-electron systems and other complex materials.