Linked formula

You Might be able to get the effect you want by using the INDIRECT() function.
With this function you can construct a text representation of a cell address or a range.

Thus INDIRECT("A1") returns the value in the cell A1,
and SUM(INDIRECT("A1:A6")) returns the sum of the cells A1 to A6.

What you can now do is set B1="A1:A6" then use SUM(INDIRECT(B1)).
So B1 contains the text representation of the range of cells you want to sum
and the eventual result is the sum of the cells A1 to A6.

If you also included the OFFSET() function it should be possible to construct a formula that will allow all the required ranges to be altered in response to the value of B1.

Thus set B1="A1"
then SUM(OFFSET(INDIRECT(B1),0,0,6,0))

Mark