The court gave me custody of my nephew three years ago. 

I want to adopt him, can I?

Ultimately you will need to file a petition for adoption. If the parents of the child would like to conditionally surrender to you this will qualify as a private adoption and can be done with the guidance of an adoption attorney.

If the parents of the child are not on-board with you adopting the child, you will need to file a termination of parental rights with the goal of kinship adoptions.

Unfortunately, you will bear the responsibility for the court costs since the agency/department is not involved. If you can afford one, hiring an adoption attorney is advisable, if you cannot afford one you can apply for attorney to be appointed via the family court clerk.