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Abstract We show how to treat the superconformal algebras with eight Poincaré super-charges in a unified manner for spacetime dimension 2 < d ≤ 6. This formalism is ideally suited for analyzing the quadratic Casimir operator of the superconformal algebra and its use in deriving superconformal blocks. We illustrate this by an explicit construction of the superconformal blocks, for any value of the spacetime dimension, for external protected scalar operators which are the lowest component of flavor current multiplets.