Learn Russian: К тому же скрипка и виолончель звучат подобно голосу человека. - Furthermore, the violin and the cello sound like a human voice.

It is triggered by the preposition подобно (like, similar to). When used as a preposition of comparison, подобно requires the Dative case for the object being compared to. Here, the instruments sound similar "to the voice" (голосу).

I know тому is the Dative of то (that), but how does К тому же mean "furthermore"?

It is a fixed phrase that literally translates to "to that same [thing]". It is a very common B2-level connector used to say "besides", "moreover", or "furthermore" when adding a new point or argument.

Is подобно always a preposition requiring the Dative case?

Not always. It can also be a short-form neuter adjective or an adverb meaning "similarly". However, when you use it to compare an action to a specific noun, as in this sentence, it acts as a preposition and forces that following noun into the Dative case.

Why does the sentence use the Genitive noun человека instead of the adjective человеческий?

Both are perfectly fine! You could say подобно человеческому голосу (using the adjective in the Dative case to match the noun) and it would mean the same thing. Russian often uses a noun in the Genitive case (голосу человека - "voice of a human") where English might use an adjective, which can sound slightly more poetic or formal.