If for the natural numbers $$a, b, c, a^{3} + b^{3} + c^{3} = 8072$$ and $$a : b = b : c = 3 : 2$$, then $$a =$$

$$a,b,c,a^{3}+b^{3}+c^{3}=8072$$ and $$a:b=b:c=3:2$$ then $$a= ? $$

let $$\frac{a}{b}=\frac{3}{2}times\frac{3x}{3}$$ and $$\frac{b}{c}=\frac{3}{2}times\frac{2x}{2}$$

then we get 

$$a=9x,b=6x,c=4x$$

now put the value of a,b,and c in equation $$a,b,c,a^{3}+b^{3}+c^{3}=8072$$

now we have eq $${9x}^3+{6x}^3+{4x}^3=8072$$

then we get $${729x^3+216x^3+64x^3}=8072$$

then $$1009x^3=8072$$

$$x=2$$

put the value of x and we get 

$$a=18,b=12,c=8$$   answer