Flooring Cubes

Algebra Level 3

Determine the value of

$\left \lfloor ( 3 + \sqrt{5} ) ^3 \right \rfloor$

Details and assumptions

Greatest Integer Function: $\lfloor x \rfloor: \mathbb{R} \rightarrow \mathbb{Z}$ refers to the greatest integer less than or equal to $x$ . For example $\lfloor 2.3 \rfloor = 2$ and $\lfloor -3.4 \rfloor = -4$ .