Decapitated baby birds

I have just made a horrible discovery in my garden underneath a tree. I found 3 very young dead baby birds caught in the tree branches - 2 of which were decapitated. I then found a further 2 dead babies on the floor under the tree, 1 of which was also decapitated and also found 1 of the baby's heads. All of the birds look like they had not long hatched as they are really small with no feathers. I was mortified to find this and I would like to know what could have possibly done this, as I haven't seen any cats in our garden and I would never have imagined other birds doing this. Thank you.