Search Google for “Let me make the songs of a nation, and I care not who makes its laws,” and you’ll discover a number of people think Plato said such a thing. However, as Kevin Mungons pointed out, there’s no evidence he did. How do faux quotes like this get started? They seem to come from nowhere and take on a life of their own.
I decided to track down this supposed Plato quotation and found the following in A History of Western Music:
Furthermore, the foundations of music once established must not be changed, for lawlessness in art and education inevitably leads to licence in manners and anarchy in society. For Plato the saying “Let me make the songs of a nation and I care not who makes its laws” would have expressed a political maxim; more than that, it would have been a pun, as the word nomos, with the general meaning of “custom” or “law,” was used also to designate the melodic patterns of a certain type of lyric song.
Grout, Donald J. A History of Western Music, 1973. p. 8
Notice the ambiguous “would have”: “For Plato the saying . . . would have expressed a political maxim.” It is possible that Grout could have used “would have” in the sense of “did,” but none of the footnotes near the quotation (there is none for the quotation itself) points to such a passage. In fact, the relevant passages in the footnotes—from Plato’s Laws—actually seem to support the converse: Plato wants law to control the music. But somewhere along the line an ambitious musical-political theorist made it through page eight of A History and decided to resolve the ambiguity in his own favor.