SAMC

Using the inequality in the hypothesis we get successively: $$\begin{array}{rl}& f\left(x_1\right)+f\left(x_2\right)+af\left(x_3\right)\ge a^{2}f\left(x_1+x_2+x_3\right)\\ & f\left(x_1\right)+af\left(x_2\right)+f\left(x_3\right)\ge a^{2}f\left(x_1+x_2+x_3\right)\\ & af\left(x_1\right)+f\left(x_2\right)+f\left(x_3\right)\ge a^{2}f\left(x_1+x_2+x_3\right)\end{array}$$ Add all and get: $$(a+2)\left(f\left(x_1\right)+f\left(x_2\right)+f\left(x_3\right)\right)\ge 3a^{2}f\left(x_1+x_2+x_3\right)$$ and the conclusion follows.