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 $A, B$ 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 $D, E$. Then $C D \cdot C E=$
4.36.

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

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