Let $n$ be an integer greater than $1$. In this paper, we obtained the stability of the multivariable Cauchy-Jensen functional equation

$$nf(x_1+\cdots +x_n,\frac{y_1+\cdots +y_n}{n})=\sum _{1\le i,j\le n}f(x_i,y_j)$$

in Banach spaces, quasi-Banach spaces, and normed $2$-Banach spaces.