When you raise a kid, there's not only the cost of delivering the baby at the hospital, but also the child-rearing costs.
この場合、次のような言い方ができますよ。
ーWhen you raise a kid, there's not only the cost of delivering the baby at the hospital, but also the child-rearing costs.
「子育てをするとき、出産費用だけでなく養育費用もかかる」
not only the cost of delivering the baby at the hospital but also the child-rearing costs のように言えます。
cost of delivering the baby で「出産費用」
the child-rearing costs で「養育費」
ご参考まで！
カナダ 
