Anyone?

Here is one far out, impractical solution:
Add a helper column (Seq), so your data looks like this:
Seq Mon
1 1
2 8
3 5
4 6
5 3
6 8
7 1
8 3
9 7
10 4
Tue

Name the Seq, Mon and Tue ranges.
The sum for Mon is this array formula
=SUM((Seq<=MAX(ROW(Mon)-ROW(INDEX(Seq,1))+1))*Mon:Tue)
For Tue:
=SUM((SeqMAX(ROW(Mon)-ROW(INDEX(Seq,1))+1))*
(Seq<=MAX(ROW(Tue)-ROW(INDEX(Seq,1))+1))*Mon:Tue)
The data may be sorted without affecting the results if
Seq is included in the sort.