Beat sugar and butter together in a large bowl with an electric mixer until light and fluffy. Add eggs and vanilla; beat well. Add flour mixture, about 1/2 cup at a time, mixing until well blended. Pour batter into the prepared pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 30 minutes. Pierce cake all over with a fork; let cool to room temperature.
Mix whole milk, condensed milk, and evaporated milk together in a bowl; pour over the top of the cooled cake and allow to soak in.
Whip cream, remaining 1 cup of sugar, and 1 teaspoon vanilla in a chilled glass or metal bowl with an electric mixer until thick. Spread over the top of the filling. Keep cake refrigerated until serving.