8.25 part (b) is just a little trial and error to find an example of a solution that works.

For 8.25 part (a), the idea is to explore different mods and try to find a contradiction. I'll assume you've done this a little bit already, so as a further hint, try looking at the equation using mod 8, and see if you can narrow down the possibilities for $y$ by looking at what $y^3$ needs to be.