Is customs duty added to the cost of goods sold?

Customs duty is not a part of COGS. It depends on the type of 'International Commerce Terms—incoterms' you are using from the following two types:

1. Delivered Duty Paid—DDP: In this method, you—the seller, take responsibility for paying the customs fee. This amount is charged during the checkout or is included in the final pricing of your product.
2. Delivered At Place—DAP/Delivered Duty Unpaid—DDU: The customer pays for the import fee for the shipment.