Draw the 15-square and the 17-square on graph paper. A good guess is to assume that the 8-square doesn't get cut. If so, where should it go in the 17-square? How about in one of the corners of the 17-square, say, the upper left corner.
This leaves a backwards L-shaped piece to be cut into 3 pieces that make the 15-square. But how to do it?:
Try dotting the 15-square in the lower right corner of the 17-square, leaving two rectangular pieces from the 17-square which stick out beyond the dotted 15-square. If you cut them both off, they won't fit in the remaining 6 x 6 hole. So just cut off one rectangular piece (2 x 9) from, say, the left side.
Off the top of the 17-square, try cutting more off than just the 9 x 2 rectangle. It would be great if the piece that you cut fits (without rotation) into the upper left corner of the 15-square. What you need is a funny-shaped piece, 6 high on the left and 6 long starting from the bottom left (to help fill in the 6 x 6 hole).
To fit in the length of 9 along the top left, cut down from the top of the dotted 15-square at a point 6 over from the dotted 15-square's upper right corner. If you follow this through, you get a sort of irregular c-shaped piece.
When you move this c-shaped piece into position, you see that the remaining portion of the 15-square is exactly a 9 x 2 rectangle into which you can put the rectangle that you cut off!
At least one person who has played around with these hints has been able to solve the puzzle: "Last Saturday, with your hints in hand, I solved it. Thank you for a great problem."