Using the direct and fixed point methods, we obtain the solution and prove the Hyers-Ulam stability of the $l$-variable cubic functional equation \begin{align*} &feft(um_{i=1}^{l}x_i\right)+um_{j=1}^{l}feft(-lx_j+um_{i=1,ieq j}^{l}x_i\right) =&-2(l+1)um_{i=1,ieq jeq k}^{l}f(x_i+x_j+x_k) +(3l^2-2l-5)um_{i=1,ieq j}^{l}f(x_i+x_j) &-3(l^3-l^2-l+1)um_{i=1}^{l}f(x_i), \end{align*} $l\in {\mathbb{N}}$, $l\geq 3$, in random normed spaces.