K. W. Jun and H. M. Kim [J. Math. Anal. Appl. 274, No. 2, 867–878 (2002; Zbl 1021.39014)] considered the following functional equation
Every solution of this equation is said to be a cubic function. In this paper the author considers the following functional equation
where . He shows that every solution of the functional equation above is a cubic function and he also establishes the generalized Hyers-Ulam-Rassias stability for this generalized cubic functional equation.