I'm in year 1, so that's all the data I can give you, but:

Year 1, it strongly depends on if you have to pay for childcare or not, and after that if you have to buy formula or can breastfeed the baby. I'd guess my not-in-daycare, breastfed infant is costing me $50/month right now, mostly in clothes and diapers. But I'm very fortunate to be in that situation, most people are paying many times that just for daycare. I assume this will go up slightly as we start to add more solid foods.

The biggest cost that I'm not factoring in to the above because it's hard to quantify: housing. That probably adds $500-600/month by itself to get an extra bedroom/bathroom where I'm at (HCOL).