Preheat oven to 350 degrees.
Butter 2-3 mini bundt cake mold pans (6 mini cakes per mold).
Place about a ½-¾ tsp. walnuts in bottom of each cake mold.
Mix yellow cake mix, vanilla pudding, softened butter, eggs, water and rum together with an electric mixer.
Pour into buttered molds and bake about 25 minutes or until golden brown.
Make glaze by heating butter, brown sugar and rum over medium low heat until smooth.
Remove from oven, gently turn onto a sheet pan and poke holes in the tops.
Slowly pour the glaze over the cakes, letting it absorb.