Place the cashews and apricots in a bowl. Cover generously with cold water and let soak for 2 hours at room temperature. Strain and discard the soaking water.
In a blender, purée the cashews and apricots with the dates and 4 cups (1 litre) of the water until smooth. Place a fine sieve over a bowl and pour in the cashew mixture. Add the remaining water. Cover and refrigerate for 2 hours or until very cold. The cashew drink will keep in the refrigerator for 1 week.