The human body wasn't ever designed to be sitting on a bike and pedaling away, so I doubt there's such a thing as "natural cadence". As other said, it may be more intentional than that based upon which gear you chose and how much force you want to push on the pedals. Pedaling-form has A LOT to do with "natural cadence" or what feels comfortable for you. Up-down mashers will be bouncing all over the place at high-RPMs, so that won't be comfortable or "natural" for them. Smooth spinners can use whatever cadence they wish really. So the same rider will tend to use lower-cadence and higher pedal-force as a beginner. After several years of riding, their cadence will be higher with less pedal-force (or they'll be faster for the same pedal-force).

I've notice when in a paceline without much power needed, I'm cruising around 80rpms. But if I'm by myself at 30mph+, it's over 100rpms. If I'm in a sprint at 35mph+, it's over 120-130rpms. A lot of the exercises I do for track-racing requires cadences in the 200rpm range.