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The smallest unit is probably a cubic Planck's length, where the Planck's length is approx 1.6*10-35 metres or 1.6*10-29 mL. Of course, you could, in principle, have a tenth (or a thousandth) of that, but it will not be a measurable volume.
The smallest unit of volume that you are likely to come across outside of a scientific lab is probably a picolitre = 10-12 Litre (a trillionth of a litre) which is the size of some of droplets used by some inkjet printers.
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