Question 935200
{{{(1/x)^3+(1/y)^3}}}


{{{(y^3+x^3)/(xy)^3}}}, and one of your equations gives you xy=b, so you can substitute:


{{{(x^3+y^3)/b^3}}};


A formula is for the sum of cubes.  You could try polynomial division to find it.
The formula in general:  {{{a^3+b^3=(a+b)(a^2-ab+b^2)}}}


Back to your expression,
{{{(x+y)(x^2-xy+y^2)/b^3}}}, and you were given x+y=a;
{{{highlight(a(x^2-b+y^2)/b^3)}}}.