To find the scale factor between two similar cylinders based on their volumes, we use the volume ratio and the properties of similar figures.
Let the volume of the larger cylinder be \( V_L = 512\pi \) inches\(^3\) and the volume of the smaller cylinder be \( V_S = 64\pi \) inches\(^3\).
The ratio of the volumes of the two cylinders is:
\[ \frac{V_S}{V_L} = \frac{64\pi}{512\pi} \]
The \(\pi\) cancels out, leaving us with:
\[ \frac{64}{512} = \frac{1}{8} \]
The volume ratio of similar objects is the cube of the scale factor. Let \( k \) be the scale factor (the ratio of corresponding linear dimensions of the smaller cylinder to the larger cylinder). Then, we have:
\[ k^3 = \frac{V_S}{V_L} = \frac{1}{8} \]
To find \( k \), we take the cube root of both sides:
\[ k = \sqrt[3]{\frac{1}{8}} = \frac{1}{2} \]
Thus, the scale factor of the smaller cylinder to the larger cylinder is:
\[ \boxed{\frac{1}{2}} \]