The volume of a cylinder is given by the formula:
\[ V_{\text{cylinder}} = \pi r^2 h \]
The volume of a cone is given by the formula:
\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \]
Since the cone and cylinder have the same radius \( r \) and height \( h \), we can relate their volumes. Specifically, the volume of the cone is one-third the volume of the cylinder:
\[ V_{\text{cone}} = \frac{1}{3} V_{\text{cylinder}} \]
Given that the volume of the cylinder is 69 cm³, we can substitute this value into the formula for the cone:
\[ V_{\text{cone}} = \frac{1}{3} \times 69 \text{ cm}^3 = 23 \text{ cm}^3 \]
So, the volume of the cone is \( \boxed{23} \text{ cm}^3 \).