Place the 4 ounces of chocolate pieces and the potato flakes in a large bowl.
Pour the hot water over the chocolate and potato flakes. Allow it to sit for 2-3 minutes until the potatoes soften and the chocolate melts. Mix well.
Add the remaining cake ingredients and blend with a hand mixer on medium low speed for about 3 minutes, scraping the bowl as needed.
Pour the batter into the prepared pan. Bake for 50-55 minutes or until the top springs back when you touch it.
Allow the cake to cool for 30 minutes, then remove it from the pan, turning it out onto a cake plate to allow it to cool completely.
In a small bowl, combine the powdered sugar and cocoa powder. Add the rum extract (or 1 tablespoon rum) and 1 tablespoon hot water. Mix well, adding in an additional tablespoon of hot water if needed to drizzle.
Drizzle the chocolate glaze over the cooled cake.
Store the cake in an airtight container at room temperature.
The calories shown are based on the cake being cut into 12 pieces, with 1 serving being 1 slice of cake. Since different brands of ingredients have different nutritional information, the calories shown are just an estimate.