Cost of Goods Sold, at income tax time, is the cost of the items you keep in inventory that are sold.
I would create and use an expense account called job expenses
To charge the customer for the expense you paid, either use a service type item you create that links to an income account, or use a double sided non inventory item also linked to an income account. I prefer the service type item.
On the P&L, income is reduced by expense to get taxable net profit.