朝の6時 seems to be consistent with using の to have one noun modify another, while 朝6時 appears to be just two successive nouns (which I wouldn't think would be a grammatically valid construction).
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I am not sure what you are really looking for. We say 朝6時, 夕方6時, 夜9時, 午前6時, 午後6時, 今月4日, 来年4月, and so on. If you want grammatical analysis, they may be considered as compound nouns, but I am not sure if understanding them as compound nouns helps you understand these expressions any better.