4. Given a moving large circle $\odot O$ that is externally tangent to a fixed small circle $\odot O_{1}$ with radius 3 at point $P, AB$ is the external common tangent of the two circles, with $A$ and $B$ being the points of tangency. A line $l$ parallel to $AB$ is tangent to $\odot O_{1}$ at point $C$ and intersects $\odot O$ at points $D$ and $E$. Then $C D \cdot C E=$ $\qquad$
4. 36 .

As shown in Figure 5, connect $A P$, $P B$, $O_{1} C$, $B O_{1}$, $P C$, and draw the common tangent line of the two circles through point $P$, intersecting $A B$ at point $Q$.

It is easy to prove that $\angle A P B=90^{\circ}$, points $B$, $O_{1}$, and $C$ are collinear, $\angle B P C=90^{\circ}$, and points $A$, $P$, and $C$ are collinear.
By the secant theorem and the projection theorem, we get
$$
C D \cdot C E=A C \cdot P C=B C^{2}=36 .
$$