Preheat oven to 350°F Butter and flour 2 8-inch square cake pans.
In a pot over medium heat, cook 1/2 cup of butter until golden brown; cool. On an ungreased baking sheet, bake the pecans until toasted, about 5 minutes. Transfer to a cutting board. On the same baking sheet, bake 1 cup of coconut, stirring until golden, about 3-5 minutes. Transfer to a board with the pecans. When cool enough to handle, chop pecans and coconut.
In a large bowl with a mixer, beat the cake mix, 1 cup of water, browned butter, eggs, and 1/3 cup rum until just blended. Increase to medium and beat 2 minutes. Stir in toasted coconut and pecans.
Divide the batter between the two pans. Bake 30 minutes or until a toothpick comes out clean. Cool on racks 10 minutes. Remove from pans; cool completely.
For frosting, in bowl with mixer at medium speed, Beat remaining butter until smooth. Beat in frosting, one can at a time, until mixture is fluffy. Beat in remaining 2 tablespoons rum.
To assemble, cut each cake layer in half horizontally. Place one layer on a serving plate. Spread with about 2/3 cup. Repeat with remaining layers and frosting. Spread top and sides with remaining frosting. Press unbaked coconut into frosting.