In this paper, we obtain the general solution and investigate the generalized Hyers--Ulam--Rassias stability for the new mixed type additive and cubic functional equation \[ 3f(x+3y)-f(3x+y)=12[f(x+y)+f(x-y)]-16[f(x)+f(y)]+12f(2y)-4f(2x). \] As some corollaries, we show that the stability of this equation can be controlled by the sum and product of powers of norms.