Volume of cube $=2\times4\times8=64\textasciitilde cm^{3}$  Side length of cube $=$$\sqrt[3]{64}$$=4\textasciitilde cm$ 
A cuboid has a length of $2\textasciitilde cm$, breadth of $4\textasciitilde cm$ and a height of $8\textasciitilde cm$. A cube has the same volume. Determine the side length of the cube. 
Options:
A: $3\textasciitilde cm$ 
B: $4\textasciitilde cm$ 
C: $5\textasciitilde cm$ 
D: $6\textasciitilde cm$ 