If $$a+\frac{1}{a}=5$$ then $$a^{3} + \frac{1}{a^{3}}$$ is:
$$a^{3} + \frac{1}{a^{3}}$$
= $$($$a+\frac{1}{a})^3 - 3(a+\frac{1}{a})$$
($$\because (a + b)^3 = a^3 + b^3 + 3ab(a + b))$$
= $$5^3 - 3(5)$$ = 110
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