If a2 + b2 + c2 + 27 = 6(a + b + c), then what is the value of 3 a^3 + b^3 - c^3 ?

Answer: Option A

$$\begin{array}{rl}& a^2+b^2+c^2+27=6\left(a+b+c\right)\\ & {\left(a-3\right)}^2+{\left(b-3\right)}^2+{\left(c-3\right)}^2=0\\ & a=3,b=3,c=3\\ & \text{root}3\text{of}{a}^3+b^3-c^3\\ & =\text{root}3\text{of}27+27-27\\ & =\text{root}3\text{of}27\\ & =3\end{array}$$