Preheat oven to 160°C. Grease a deep 22cm baba pan well.
Combine figs and marsala in a small saucepan; bring to the boil. Cool 15 minutes.
Meanwhile, beat butter and brown sugar in a small bowl with an electric mixer until light and fluffy. Beat in eggs, one at a time. Transfer mixture to a large bowl; stir in sifted flours and soda, and sour cream.
Blend or process fig mixture until it forms a smooth paste; stir into cake mixture. Spread mixture into the pan; smooth surface.
Bake cake about 1 hour. Stand in pan 5 minutes; turn onto a wire rack to cool. Dust with sifted icing sugar before serving.