Pre-heat the oven to 180°C(fan)/200°C/gas mark 6. Grease and line with baking paper a 20cm/8inch square cake tin.
Beat together the eggs, sugar, honey, oil, ginger and syrup in a large mixing bowl.
In a separate bowl sift together the flour, baking powder and ground ginger. Fold the dry ingredients into the wet ingredients until combined and finally stir in the swede.
Bake in the oven for 35-40 minutes until golden brown and a skewer inserted in the centre comes out clean. Leave to cool completely in the tin before turning out and serving.
This is fine un-iced but if you do want to ice it as I have simply mix together 100g sifted icing sugar with a couple of tablespoons of water. Add the water gradually, mixing it in as you go so it doesn't get too runny. If you put in too much water simply sift in a little more icing sugar. Pour over the cake and leave to set.