This is my idea.
First, you have to define the name for each product and each month.

I copied your data and put it in my spreadsheet, then I define the
name. For example, I gave a name "Month_1" for data in cell B2:E7 and
"Month_2" for data in cell F2:J7. Also, I gave a name "Product_1" for
data in cell B2:J2, "Product_2" for data in cell B3:J3, and so on.

Second, You should put those names in one column and one row, like
this:
Month_1 Month_2
Product_1 ***
Product_2
:
:
Product_6

Then, in cell ***, you can fill it with
"=SUM(INDIRECT($A10) INDIRECT(B$9))", where A10 and B9 is the cell
which contain the "Product_1" and "Month_1" respectively. You just
need to copy the formula  into another cells.