Find the value

Question:
Find the value

$(a-3 b)^{3}+(3 b-c)^{3}+(c-a)^{3}$

Solution:

Let $a-3 b=x, 3 b-c=y, c-a=z$

$x+y+z=a-3 b+3 b-c+c-a=0$

$(\therefore x+y+z=0) ?$

$x^{3}+y^{3}+z^{3}=3 x y z$

$=3(a-3 b)(3 b-c)(c-a)$

$\therefore(a-3 b)^{3}+(3 b-c)^{3}+(c-a)^{3}$

$=3(a-3 b)(3 b-c)(c-a)$