If $$x = \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}}$$ and $$y$$ is the reciprocal of $$x$$, then what is the value of $$(x^3 + y^3)$$?

$$x = \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}}$$
$$x = \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}} \times \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} - \sqrt{3}}$$
$$x = \frac{(\sqrt{5} - \sqrt{3})^2}{(\sqrt{5})^2 - (\sqrt{3})^2}$$
$$x = \frac{5 + 3 - 2\sqrt{15} }{2}$$
$$x = 4 - \sqrt{15}$$
$$y = 4 + \sqrt{15}$$
Now,
$$(x^3 + y^3)$$ = $$(x + y)^3 - 3xy(x + y)$$
$$(x^3 + y^3)$$ = $$(4 - \sqrt{15} + 4 + \sqrt{15})^3 - 3(4 - \sqrt{15})(4 + \sqrt{15})(4 - \sqrt{15} + 4 + \sqrt{15}$$
$$(x^3 + y^3)$$ = $$(8)^3 - 3[(4)^2 - (\sqrt{15})^2](8)$$
$$(x^3 + y^3)$$ = 512 - 24 = 488