Question 763384
We will use the identity 

{{{(a - b)^3 = a^3 - b^3 - 3*a*b(a - b)}}}  ------- (1)

{{{x - 1/x = 3}}}

{{{(x - 1/x)^3 = 3^3 = 27}}}

But by the identity (1),

{{{(x - 1/x)^3 = x^3 - 1/x^3 - 3*x*(1/x)*(x - 1/x)}}} ------- (2)

Substituting for (x - 1/x) as 3

{{{(x - 1/x)^3 = x^3 - 1/x^3 - 3*1*3}}} ------- (3)   ---> x*1/x = 1

{{{27 = x^3 - 1/x^3 - 9}}}    ------ (4)

So, 

{{{x^3 - 1/x^3 = 36}}}

:)