The volume of a cylinder is given by the formula:
\[ V_{cylinder} = \pi r^2 h \]
The volume of a cone is given by the formula:
\[ V_{cone} = \frac{1}{3} \pi r^2 h \]
Since the cone has the same height \( h \) and diameter (and thus radius \( r \)) as the cylinder, the volume of the cone would be one third of the cylinder's volume.
Given that the volume of the cylinder is \( V_{cylinder} = 27\pi , \text{cm}^3 \), we can find the volume of the cone:
\[ V_{cone} = \frac{1}{3} V_{cylinder} = \frac{1}{3} (27\pi) = 9\pi , \text{cm}^3 \]
Therefore, the volume of the cone is:
\[ \boxed{9\pi , \text{cm}^3} \]