The author examines the stability of the functional equation \( f: M \to S\) \[ 3f \left( \frac{x+y+z}{3} \right) + f(x) + f(y) + f(z)=2\left[ f\left ( \frac{x+y}{2} \right) + f\left(\frac{y+z}{2} \right) + f \left ( \frac{z+x}{2} \right) \right], \] where \(M\) is an abelian semigroup in which the division by \(2\) and \(3\) is performable and \(S\) is an abstract cone satisfying the cancelation law and \((S,\rho)\) is a complete metric space. Then it is shown that there exists an additive function \(a : M \to S\) and \(b \in S\) such that \(f(x)=a(x) +b\). Also, some applications to a multivalued version of this equation are given.