1776

Assume the third root is c, then

a + b + c = -1, a + b = -1 -c;
ab + (a + b)c = -2008, ab - c - c^2 = -2008;
abc = 232.

It is easy to see that the formula to be evaluated is

464 + 3ab(a + b) + (a + b)^2 + 2ab + (a+b)   

replace a + b with -1 -c and using abc = 232, we have

-232 - ab + c + c^2  = 2008 -232 = 1776.