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The notions of cubic soft◦-subalgebras and (closed) cubic soft ideals in BCK/BCI-algebras are introduced, and related properties are investigated. Relations between cubic soft subalgebras, cubic soft◦-subalgebras and (closed) cubic soft ideals are discussed. Conditions for a cubic soft subalgebras to be a (closed) cubic soft ideals are provided. Characterizations of cubic soft ideals are considered. R-union and R-intersection of cubic soft ideals are discussed.