Put the sugar and 1/4 cup water into a small saucepan and bring to a boil over medium heat. Cook, swirling the pan, until the sugar is completely dissolved.
Put the raspberries and strawberries into a blender jar and pour the hot sugar syrup over them. Puree the berries just until liquefied. Pour the mixture through a fine mesh strainer set over a bowl to strain out the seeds.
Transfer the sauce to a pitcher and pour over ice cream or sliced pound cake. Store the leftover sauce in an airtight container for up to 3 days.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.