Is it obligatory to return the increase to the brother, paid as the price for gold, after the questioner learned that delaying the payment for gold beyond the time of sale is considered usury, knowing that the brother has already disposed of the gold he bought?

It is not permissible to sell gold with a delayed receipt of the price, due to the Prophet's (peace be upon him) saying: "Gold for gold... hand to hand." The contract that took place between you and your brother is فاسد (invalid/corrupt).

The original ruling for an invalid contract is that ownership is not established, and the seller must return the price, and the buyer must return the goods, unless it is impossible to return them. If returning them is possible, it is obligatory.

However, if returning them is impossible because one of the parties has disposed of what they received, then, according to the more preponderant opinions, returning them is not obligatory.

Therefore, you are not obliged to return the money you took to your brother. You should seek forgiveness and repent, and be keen to learn the Islamic rulings before engaging in financial transactions.