b
(b) $\Delta = \left| {\,\begin{array}{*{20}{c}}{2(a + b + c)}&0&{a + b + c}\\{c + a}&{b - c}&b\\{a + b}&{c - a}&c\end{array}\,} \right|$
by ${R_1} \to {R_1} + {R_2} + {R_3}$
$\Delta = (a + b + c)\,.\,\left| {\,\begin{array}{*{20}{c}}2&0&1\\{c + a}&{b - c}&b\\{a + b}&{c - a}&c\end{array}\,} \right|$
On expanding,
$ - (a + b + c)\,({a^2} + {b^2} + {c^2} - ab - bc - ca)$
= $ -(a^3 + b^3 + c^3 - 3abc) = 3abc - a^3 -b^3 - c^3$
Trick : Put $a = 1,\,b = 2,\,c = 3$ and check it.