14. Find the smallest real number $m$, such that for any positive real numbers $a, b, c$ satisfying $a+b+c=1$, the inequality $m\left(a^{3}+b^{3}+c^{3}\right) \geqslant 6\left(a^{2}+b^{2}+c^{2}\right)+1$ holds. (2006 China Southeast Mathematical Olympiad)