  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.
