Hand raising baby birds is pretty hard as they require a lot of feedings during daylight hours.
Cardinals are seed eaters usually but the adult birds do also take some insects and they mush up the food in their crops for the babies.
You may want to contact a wildlife rehabilitator to take this on for best results for the babies
http://www.tc.umn.edu/~devo0028/contact.htm
Here are a couple more sites on baby birds including commercial and home made formulas
http://www.2ndchance.info/seedeater.htm
http://www.birds.cornell.edu/AllAboutBirds/attracting/challenges/orphaned
Both parents feed the hatchlings so your nest of babies may have been cared for by the father.
Hope this helps you!
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