The same technique as for segment tree: you store additional variable for each SQRT block named toset. It stores value to which elements of block should be changed. When you access separate elements of block, you just update the whole block in and recalculate sum of its elements. I've changed your example a bit (I split different blocks with | and write toset above the array):

 null    null   null
1 2 3 | 4 5 6 | 7 8

1. Change the values from 3 to 6 to 10. We need some elements of block 1 and the whole block 2. So, we can set toset[2] to 10 instead of running down all its elements:

 null     10     null
1 2 10 | 4 5 6 | 7 8

1. Change the values from 6 to 8 to 100. We need to access only a part of block 2, so it's neccessary to update its elements with value of toset[2]. Block 3 is required entirely, so we use toset[3].

 null     null      null
1 2 10 | 10 10 10 | 7 8 

 null     null       100
1 2 10 | 10 10 100 | 7 8 

1. Get the sum of elements from 2 to 8. We do it in the following way: calculate elements 2 and 3 separately (as we don't need the whole block 1), add sum of block 2 and then we add 100*2, because we know that all elements of block 3 should be 100 and it contains 2 elements.