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We will prove the general solution of the following cubic functional equation 4{f(2x+ y + z) + f(x+ 2y + z) + f(x+ y + 2z)} = 27f(x+ y + z) + f(−x+ y + z) + f(x− y + z) + f(x+ y − z) + 12{f(x) + f(y) + f(z)} and investigate the stability of a cubic Lie ∗-derivation associated with the given functional equation. AMS Subject Classification: 39B82, 39B62

HYERS-ULAM-RASSIAS STABILITY OF LIE $*$-DERIVATIONS OF A CUBIC FUNCTIONAL EQUATION WITH THREE VARIABLES