There are some different methods to make marbled pattern in a cake. I have tried some methods, and I have found mixing two coloured batter in a mixing bowl is the easiest. After roughly mix them, I just pour the batter into a cake tin. You might prefer your favourite method.

Cake Tin

Standard Loaf Tin

Ingredients

125g Butter *softened
125g (OR 1/2 cup) Caster Sugar
3 Eggs *about 125g, must be at room temperature
1/2 teaspoon Vanilla Extract *OR 1 teaspoon Brandy, Rum, Whisky, etc.
150g (OR 3/4 to 1 cup) Self-Raising Flour
1 tablespoon Instant Coffee Granules
1 tablespoon Hot Water

Method
  1. Preheat oven to 170°C. Grease a loaf tin and line the base and sides with baking paper.
  2. Beat the softened Butter in a mixing bowl with a whisk or an electric mixer until smooth. Add Sugar and beat until creamy.
  3. Add Eggs, one at a time, beating well after each addition. If the Eggs are not warm enough, the mixture will curdle. If that happens, try to stand the bowl in warm water, stirring constantly, for 30 seconds, then continue beating until the batter becomes smooth and creamy.
  4. Add Vanilla and gently fold in Flour with a spatula or large metal spoon until just combined. *Note: Batter should be thick. Add extra Self-Raising Flour if required.
  5. Transfer 1/3 of batter to a bowl. Mix Instant Coffee Granules and Hot Water in a small bowl, add to the 1/3 batter, and mix well. *Note: You might think the colour is too light, but it will turn dark when baked.
  6. Pour the coffee flavoured batter to the remaining 2/3 batter, and roughly mix, no more than twice. Pour the batter into the prepared loaf tin and smooth the surface. *Note: DO NOT damage the marbled pattern. You only need to roughly smooth the surface, as the batter will flatten by itself.
  7. Bake in preheated oven for 30 to 35 minutes or until cooked through. Transfer to a wire rack and cool. *Note: You may wish to create the centre crack, but this cake might not crack.