No, you must not include the same costs in both sections, or you will double-count the deduction. You should enter the cost of the raw metal under "Total purchases" in the Inventory section so it can be factored into your Cost of Goods Sold. The service fee paid to the casting house for their labour should be entered as a Subcontract or Professional fees expense. Essentially, if an item is a physical component of your finished jewellery, it belongs in Inventory; if it is a service or a general supply that doesn't become the product itself, it belongs in Expenses.
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