Beer needs malt and hops. You can produce alcohol with yeast and cane sugar, it just wouldn't be beer. Fermented cane sugar that's then distilled is how rum is made.
It is unlikely to taste very good. Lots of breweries are using cane sugar (or other sugar) to produce a base for "hard seltzer", but without fruit or other additives it doesn't taste very good. Like VERY bad white wine.