In a medium mixing bowl, combine sugar, instant espresso/coffee, and water. Immediately after pouring into the bowl, use a whisk (or whisk attachment of a hand mixer) to whip the coffee until it begins to lighten in color.
Continue to whisk until the coffee reaches the consistency of still peaks (like meringue). Set aside and prepare your cups for serving. Add ice to three cups or glasses.
Add equal amounts of milk to each glass, then add 1 oz of irish cream to each cup or glass.
Lastly, use a spoon or small spatula to divide the whipped coffee mixture atop each glass. Serve immediately.