Cane sugar is ordinary table sugar (sucrose), and its brewing role sits close to dextrose's: fully fermentable, contributing almost no unfermentable residue, and used specifically to add alcohol strength without adding the body and malt character an equivalent gravity boost from more base malt would bring. Belgian brewing has leaned on this technique for generations, and it's the reason a well-made tripel can land at 8-9% ABV while still drinking lighter-bodied than many session beers half its strength.
Yeast breaks sucrose down into glucose and fructose before fermenting it, a step that happens quickly and doesn't meaningfully change how the sugar behaves compared with dextrose in practice — both ferment out close to completely, leaving little behind. The main practical difference brewers report is subtle rather than dramatic: cane sugar can carry a faint flavour echo of its origin at higher dosages, where refined dextrose reads more neutral. Cane sugar's role in the boil is entirely separate from its use as a bottling-time priming sugar (see the priming sugar calculator for that calculation) — the same sugar, used at two different points in the process for two different reasons, one for strength and dryness, the other for carbonation. Dextrose is the closest substitute where cane sugar specifically isn't the goal, and the two are close enough in practice that many Belgian-style homebrew recipes simply specify "sugar" without insisting on one over the other.