Steps:
1. First layer's edges and corners.
2. Build upwards, but leave one edge pair on the last layer empty.
3. Rotate that free slot to the bottom layer, then fill in the centres.
4. Insert last edge pair, optionally rotate back.
I assume this method will work about as well with nonmagnetic or conventionally-magnetised cubes. Haven't tried, though.
For 5³, it's way faster to just build the full centre instead of leaving it to the end. Haven't had the courage to fully disassemble a 6³ or 8³ yet, so idk what works best for those. Haven't had a need to disassemble a 7³ recently either, but I think I used pretty much this method the last time; probably faster to build the full centre too, just like on 5³.
Halfway thinking of making some puzzle theory vids in the coming weeks; 2-gen corner permutation is one of the topics I have in mind. If I actually get around to doing that (big question mark), I might ask for people to review a draft version and make sure it's not overly abstract or outright incomprehensible to a "lay" audience; PM me if you're interested.
