Fame is like a drug that I've taken too much of
Drake can’t get enough of his fame which means he is addicted to the fame, so he always wants to get more of it. You can compare it to being on drugs, from which people also can’t get enough.
Homophone: “Famous like a drug"
He does also smoke a lot of ganja, which is why this double entendre fits him well. Everybody knows what weed is, therefore the drugs he takes are just as famous as he is as a person.
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