ÖMO 1983 Problem 2

Let $x_1,x_2,x_3$ be the roots of: $x^3-6x^2+ax+a=0$ . Find all real numbers $a$ for which $(x_1-1)^3+(x_2-1)^3+(x_3-1)^3=0$ . Also, for each such $a$ , determine the corresponding values of $x_1,x_2,$ and $x_3$ .