Actually, this happens all the time
if we're not restricting ourselves to humans
. In the animal kingdom, intraspecific cannibalism
is quite a common occurence, and often happens between creatures of the same age/cohort
. Lizard and snake siblings will eat one another from time to time, but this happens most often with both marine and freshwater fish
Generally, what happens is that some baby fish get a good start to life because they either hatch earlier than their siblings or are blessed with a larger yolk sac, which means that during their larval stage they can grow more quickly and to a greater size. With this advantage, they begin to make use of certain prey resources more quickly, and thus the small difference in size at the beginning of life become a very large difference in size only a couple of months later. For a lot of freshwater species, by the end of the first year of life, one sibling can be three times longer than another, making the latter a perfect target for the former.
However, I should state that if we are talking about human babies, I think the answer is: 'no.' First, human babies don't have teeth, and gumming your fellow baby to death would be quite difficult. Second, most babies couldn't care for raw meat, so probably wouldn't even try. And thirdly, one crying baby normally sets all others in the vicinity off, so if baby A were to bite baby B, B would cry, making A cry, making A's eating of B difficult.
Now, if we're talking about toddlers (age 18 months and up), that's an entirely different story. They tend to have lots of teeth, and baby teeth are remarkably sharp. Furthermore, at this age children are on to solid food, and many prefer meat to vegetables and cereals. Most importantly, however, at this age children have acquired a sense of self and of their own power, but haven't developed the capacity for empathy. Therefore, a particularly aggressive and hungry 18 month old may indeed be capable of taking out a partner at daycare.
I can see it now: "Tonight, on Fox: When babies attack other babies and no one's around to see the attack and when the baby eats the other baby .... etc., etc. Now your host, Geraldo Rivera!"