Mix sugar, water, and cocoa in a small saucepan. Bring to a boil over medium heat, stirring occasionally. Reduce heat to low and simmer, stirring occasionally, just until sugar and cocoa are completely dissolved. Remove from heat and cool to room temperature.
Pour into a clean 2-quart glass container. Stir in vodka and vanilla bean. Cover tightly; keep in a cool, dark place for 14 days, shaking container thoroughly every 2 days.
Strain liqueur through a moist paper coffee filter into a clean glass container. Straining will take a couple of hours as residue is very thick. Change filter halfway through. If residue remains, strain again immediately.
Cover tightly; let liqueur age in cool, dark place at least 1 month.