Step 1: Cylinder Curved Surface Area Formula.
The formula for the curved surface area (C.S.A) of a cylinder is:
\[
\text{C.S.A} = 2 \pi r h
\]
where \( r \) is the radius and \( h \) is the height.
Given C.S.A = 264 cm\(^2\) and \( h = 14 \) cm, substitute these values into the formula:
\[
264 = 2 \times \frac{22}{7} \times r \times 14
\]
Simplify to find the radius:
\[
264 = \frac{22}{7} \times 28 \times r \implies r = \frac{264 \times 7}{22 \times 28} = \frac{1848}{616} = 3
\]
Therefore, the radius \( r = 3 \) cm.
Step 2: Cylinder Volume Formula.
The volume \( V \) of the cylinder is calculated using:
\[
V = \pi r^2 h
\]
Substitute \( r = 3 \) cm and \( h = 14 \) cm:
\[
V = \frac{22}{7} \times 3^2 \times 14 = \frac{22}{7} \times 9 \times 14 = 396 \, \text{cm}^3
\]
Final Answer: \[ \boxed{396 \, \text{cm}^3} \]