Selected Answer
The task is easier if you reverse your logic. It isn't several cells you wish to sum up in another spreadsheet. Instead, it is the other spreadsheet which is to show the sum of several cells from your list. Therefore you need a formula in the other spreadsheet, to be precise, in the cell where you wish to see the total. For example,
=SUM(Sheet1!$A$3:$A13)
Here, "Sheet1" is the name of the tab with the list. Observe that it is followed by an exclamation point. If there are blank spaces in the name, surround the name with apostrophes, like, =SUM('My Sheet'!$A$3:$A$13)
If the cells you wish to sum up are not in a contiguous range you can expand the system like this
=SUM('My Sheet'!$A$3:$A$6,'My Sheet'!$A$8:$A$13)
or like this
=SUM('My Sheet'!$A$3,'My Sheet'!$A$8:$A$10,'My Sheet!$A$13)
or
=SUM('My Sheet'!$A$3:$A$6) +'My Sheet'!$A$13