In this work, we examine the Hyers-Ulam stability of the cubic functional equation \(\begin{aligned}&2m g(\varrho +m\sigma )+2g(m\varrho - \sigma )- (m^3+m)\{g(\varrho +\sigma )+g(\varrho -\sigma )\} \\&\quad - 2(m^4-1)g(\sigma ) =0, \end{aligned}\) with a fixed positive integer m in the context of \((\beta , p)\) -Banach space, using the alternative fixed point approach and the direct method. We also verify the Hyers-Ulam stability for the cubic functional equation in non-Archimedean \(\beta\) -normed space. Our findings enhance and extend many of the results in the existing literature.
