Preheat the oven to 350 degrees F. Grease and flour a 10-inch tube pan. Sprinkle nuts over bottom of pan and set aside.

In a large bowl, beat butter and sugar at medium-high speed of an electric mixer until light and fluffy. Add eggs and yolk one at a time mixing well after each addition. Add vanilla and mix to combine. Gradually add rum beating until blended (batter will look curdled).

In a small bowl, stir together flour, baking powder, baking soda, and salt. Add flour mixture alternately with whipping cream, beginning and ending with flour mixture. Pour batter into the prepared tube pan. Bake for 55 to 60 minutes or until a cake tester inserted in the center of the cake comes out clean.

Cool the cake in the pan on a wire rack for 15 minutes. Pierce cake multiple times using a metal or wooden skewer. Pour rum syrup over the cake. Let cake stand for 45 minutes. Remove cake from the pan and cool completely on a wire rack.

Melt butter in a 2-quart saucepan over medium-high heat. Stir in sugar and rum. Bring to a boil, stirring constantly. Reduce heat to medium and cook 8 to 10 minutes, stirring often, until slightly thickened. Cool 10 minutes.