There is no direct relationship. A millimeter is a length (a distance), like a foot or a mile, whereas a liter is a volume (an amount that you can hold in a bag or a bottle), like a gallon or a bushel. Your question is a lot like asking "How many inches can your gas tank hold ?"
If you want a cube that can hold a liter, it has to be 100 millimeters (about 3.94 inches) long, wide and high.
If you want a sphere that can hold a liter, it has to have a diameter of about 124 millimeters (about 4.88 inches).
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