If x + y + z = 6, then the value of (x - 1)3 + (y - 2)3 + (z - 3)3 is?

Answer: Option D

$$\begin{array}{rl}& x+y+z=6\\ & {\left(x-1\right)}^3\text{ + }{\left(y-2\right)}^3\text{ + }{\left(z-3\right)}^3\\ & \therefore \text{As, }x+y+z=6\\ & \text{Take values}\\ & x=1\\ & y=2\\ & z=3\\ & \left(1+2+3\right)=6\\ & \therefore {\left(1-1\right)}^3\text{ + }{\left(2-2\right)}^3\text{ + }{\left(3-3\right)}^3\\ & =0\end{array}$$
Now assume values in options.
Option 'D' satisfies the given relation.
Hence 'D' is correct.