I taught myself to cube in '80 or '81. Bought a cube and worked it out for myself. Later on, I worked out the 4x4 and the 5x5 for myself too. I consider the Rubik's cube to be a puzzle, and that to use anyone else's method is cheating.
I realise that I am almost entirely alone in this viewpoint!

My fastest time for a 3x3 was an unimpressive mid-40s seconds for decades, until my friend Tom lubed my cube for me (that's probably cheating too

) , and then I got it down to sub-30. No idea what my best 4x4 time is, but my average 5x5 time is... somewhere around 20 minutes!