First, you should write =SUMPRODUCT(A1:A3,B1:B3) instead, which is normally-entered.

Second, =SUM(A1:A3*B1:B3) seems to work only if it is entered in row 1, 2 or 3. It is interpreted as =SUM(A1*B1), =SUM(A2*B2) or =SUM(A3*B3) respectively. And if that is the intent, there is no reason to uses the SUM function in that context. Simply write =A1:A3*B1:B3.

That interpretation is most useful for named ranges, e.g. "cost" defined as A1:A3 and "qty" defined as B1:B3, and your intent is to enter the formula =cost*qty for each of 3 transactions in rows 1, 2 and 3.

The point is: if you normally-enter =SUM(A1:A3*B1:B3) into any other row, you will get a

#VALUE result, correctly informing you that the form is incorrect.