When the brochah shehakol is made on gum, is the brochah being made on the gum base, or the flavoring? (I'm assuming one makes a brochah on gum, but maybe not: see http://torahmusings.com/2010/11/chewing-gum-bracha-or-no-bracha/.)
It is on the flavouring. According to the famous Birkas Hashem (maamarim 1, quoted by the responsum on the topic - see below), there wouldn't be a need for a Bracha on flavourless gum.
People don't typicaly chew such gum today, choosing only flavoured gums.
While there are poskim (Birkas Hashem, maamarim 1) that hold that one does not recite a bracha before chewing gum, most follow R’ Ovadia Yosef (Yabia Omer 7 OC:33) and R’ Ephraim Greenblatt (Rivevos Ephraim 6:80:2) and recite shehakol.