Im assuming you mean 26 miles? That's four hours for your average runner? Most cyclists can get away with barely eating for four hours too, if they're riding a moderate pace. But if a cyclist finishes a century around 4 hours, he/she is riding very very intensely & will need to eat.

Its very simple. It's not about whether you "should" eat while cycling or whether you "shouldn't". It's about the duration & intensity of your cycling relative to your personal max and the total amount of carbohydrate you have stored in your muscles & liver. How well-trained you are to the effort- the better trained you are, the more you will be able to metabolize fat.

Riding intensely for >3-4 hours: eat on bike, as much as you can (you still won't be able to keep up with calorie demands, maybe you can get 200-250 food cal/hr into you, beyond that digestion while riding is iffy). If you're sweating a lot, replace electrolytes. No matter what, replace water. Recovery drink afterwards no matter what the duration of the ride, the utility of a recovery drink relates to the intensity of the ride, ie whether you broke down muscle.

Riding intensely for <3-4 hours: eat if you're hungry. Replace electrolytes if sweating but you have a good amount of wiggle room & will probably get away with just water. Recovery drink post-ride.

Riding non-intensely you can eat & drink less. The longer the ride, the more any deficits will catch up with you.

Organized centuries may have a wide variety of foods but that doesn't mean you need to eat it all.