On a cubic–quadratic equation relative to elliptic curves

We investigate the Hyers–Ulam stability of the following cubic–quadratic functional equation relative to elliptic curves f(x+ y+ z, u+ v+ w) + f(x+ y− z, u+ v+ w) + 2 f(x, u− w) + 2 f(y, v− w) = f(x+ y, u+ w) + f(x+ y, v+ w) + f(x+ z, u+ w) + f(x− z, u+ v− w) + f(y+ z, v+ w) + f(y− z, u+ v− w). The function f(x, y) = x³+ ax+ b− y² having level curves as elliptic curves is a solution of the above functional equation.