Step 1: Recall the morphology clue. Molluscum contagiosum is famous for large intracytoplasmic inclusion bodies, a hallmark of cytoplasmic replicating DNA viruses.
Step 2: The poxvirus family is the group of large brick shaped double stranded DNA viruses that multiply in the cytoplasm, and molluscum contagiosum virus sits squarely within it.
Step 3: Rule out the rest. Herpesviruses replicate in the nucleus with intranuclear inclusions, picornaviruses are tiny RNA viruses, and adenoviruses are non enveloped icosahedral DNA viruses, none matching the cytoplasmic poxvirus profile.
Step 4: The cytoplasmic inclusion bearing, brick shaped agent of molluscum is a poxvirus.
\[\boxed{\text{Poxviruses}}\]