Combine peanut oil, 1 cup cane syrup, and next 3 ingredients in a large bowl, beating with a mixer on medium speed until blended. Add eggs, one at a time, beating until blended after each addition.
Combine flour and next 5 ingredients in a medium bowl; slowly add flour mixture to egg mixture, beating at low speed until blended. Pour batter into 3 greased and parchment-lined 8-inch round cake pans.
Bake at 350° for 20 to 25 minutes or until a wooden pick inserted in the center comes out clean. Cool in pans on wire racks 10 minutes, remove from pans, and cool on wire racks.
Prick cake layers with a wooden skewer; brush remaining 1/4 cup cane syrup over tops. Spread Burnt Sugar Meringue between layers and on top of cake.