A systematic study of fixed point theorems in nonlinear analysis is given by \textit{G. Isac} and \textit{Th. M. Rassias} [Int. J. Math. Math. Sci. 19, No. 2, 219--228 (1996; Zbl 0843.47036)]. Using the alternative fixed point theorem [see \textit{J. B. Diaz} and \textit{B. Margolis}, Bull. Am. Math. Soc. 74, 305--309 (1968; Zbl 0157.29904)] and known techniques, the authors prove the stability of the following \(n\)-dimensional cubic functional equation in Banach spaces and Banach modules. \[ \begin{multlined} f\left(\sum_{j=1}^{n-1}x_j+2x_n \right)+ f\left(\sum_{j=1}^{n-1}x_j-2x_n \right) + \sum_{j=1}^{n-1}f(2x_j)\;\\ = 2f\left(\sum_{j=1}^{n-1}x_j \right)+ 4\sum_{j=1}^{n-1}\left(f(x_j+x_n)+f(x_j-x_n)\right), \end{multlined} \] where \(n \geq 2\). They also show that a function \(f\) between real linear spaces satisfies the above functional equation if and only if it is cubic, namely it satisfies \[ f(2x+y)+f(2x-y)=2f(x+y)+2f(x-y)+12f(x). \]