x3+y3+z3=8072. x:y=y:z::3:2 y=?

Understand na bro. I think this is correct

x:y=y:z=3:2
Hence, x:y:z=9:6:4
Given- x3+y3+z3=8072
Put the value of x,y,z by assuming x=9a, y=6a, z=4a Understand na bro
{(9a)3+(6a)3+(4a)3=8072
729a3+216a3+64a3=8072
1009a3=8072
a3=8 a=2
Hence, x=9a=18, y=6a=12, z=4a=8.

x/y = 3/2
x = y*3/2
x3 = y3 * 27/8 ----- 1
y/z = 3/2
z = y*2/3
z3 = y3 * 8/27 ------2
put 1 and 2 in given eqn
y3 * 27/8 + y3 + y3 * 8/27 = 8072
y3 * (1009/216) = 8072
y3 = 8072*216/1009
y3 = 8*216
y = 2/6
y = 1/3

xyz are positive integers