Solve this puzzle! (hard)

[deadly7]

2+1+3+6+5+1+2+6 = 26
3+5+6+5+3+6+3+4 = 35

etc etc

[TeHFoOoL]

From the authors website:

"Below is a very special grid, around each shaded number are 8 white squares. However, each white square should have a number from 1 to 7. Once filled in, these 8 numbers will sum to the shaded number. In addition, once completed correctly, no row nor column will contain a duplicate number within a white square. For example, the top row may be 5 6 4 2 3 1 7, etc. This is [site name removed] most difficult puzzle, but is solvable without the aid of a computer"

Right-click image. :]