Wish I could figure out the layout pages, just can't muster the patiences.
Anyway, what came to my mind was, 5 - 1 - 6 - 3 top left corner - 4 bottom right corner - 2 bottom left corner - 8 top left corner, stun over for the 7 break.
One thing that you'll find when you actually go through the run on the cuetable is that you'll make similar mistakes to those you would on a real table. You realize after you've drawn your line that you should have played a slightly different position because you trap yourself into tougher shots on later balls, or something similar. I highly recommend you get into it. Your bad habits show up. It teaches you while you're doing it.
My first crack at it. There is probably a more simple way to run this out, but this is the first to come to mind. more than likely, my cue ball would drift a bit playing all these relaxed draw shots, and would have to re-evaluate. (not to mention my table drawing skills suck). If I missed position after the first shot, instead of the 4, I would use the 2 to get back on the 4, then deal with trouble 6 on the rail. The 1 at the end of the sequence, the leave would be difficult to get without using rails, so I probably would do it different.