I suggest you use a cursor to do this as you cannot do that with just one update statement.
select order_number, sum(item_qty*cost_each) from child group by order_number order by order_number
This would result in what you are looking for. May be use can use INTO clause there in the above select statement to store it in to a separate table. Else go for a cursor based solution. That should be the right one.
Hope that helps.
- Vijay G
Strive for Perfection