I saw the question, but I thought if I said an almost exact same thing, people would think I was silly, and I've only had canes for a little over a year. I've seen several different cane Begonias doing this. Almost white blooms if some show up while inside for winter. Pink or even red outside. Still obviously proof out there in some form, but yet another failure to prove I'm crazy.
I also suspect it could have something to do with fertility. I don't fertilize anything inside for winter, and use tap water. So outside, many Begonias get to play in the ground, and even if in a pot, get rain water, occasional packaged fertilizer, and this summer, banana water (diluted, pureรฉ banana peels, whole clearance 'nanas. If Gramma's suggestion works so well on rose bushes, why not share the love a bit more? I don't worry about measuring anything, getting it on my hands, critters, pet. So far, it seems to be just short of magic after a couple recent applications to potted plants. One never knows if a plant just happened to be ready, or if something like that is what did it, know what I mean? More research is worthy, IMO, I'll say that much. I like cheap, safe, easy, and natural. Flood killed a lot of plants in the ground, so that was unfortunately inconclusive and disappointing. Go figure, last summer it didn't rain at all. They're back to cuttings, which is kind of ironic. At least I got a chuckle and anecdote out of it. Yay, right?
The leaves also seem somewhat schizo, depending on light, but that's common with almost any kind of variegation.
Hey, I posted the pic but forgot to ask a question that was supposed to go with it. Is the Begonia that is similar to Joejoe's something that shows up in the pic? It was never happy by itself, like your beautiful plant, but tiny propagated pieces in mixed pots are finally coming into their own a bit by now. I think I've still got at least 1 rooted plant of every kind. What a long, strange trip it's been...