RMO 2014 M2

The roots of the equation $$x^3-3ax^2+bx+18c=0$$ form a non-constant arithmetic progression and the roots of the equation $$x^3+bx^2+x-c^3=0$$ form a non-constant geometric progression. Given that $a,b,c$ are real numbers, find all positive integral values $a$ and $b$ .