Rephrasing your question so it's more obvious:
133286
First = 1, last = 6: Sum = 7
Remaining
3328
First = 3, last = 8: Sum = 11
Remaining
32
First = 3, last = 2: Sum = 5
And it's clear that this is the same task repeated - so make your code reflect that.
The first thing to do is to put the code to work out the sums into a method, so you can call it repeatedly. Pass it the array and the start index, have it return the sum, and it's pretty simple to do.
When you have that working, add your loop to call it repeatedly.
Start by making that call the array the right number of times - sort out when the loop should exit first, and do something useful with the result your method return. What exactly is "useful" will depend on you, the environment yoru code is to run in, and what exactly you want to do with the result.
For example, a Console app may want to print each result, but a more general app may want to add them to a collection (a List or an Array maybe) for later processing. We don't know what your tutor wants you to do!
Then make it pass an incrementing start index to method, and you're done.
Think about the task, try it on paper, and you'll get it done in very little time.