This is a bit tricky because "quart" can be a US liquid quart or an imperial quart, and they have different volumes. Here's the breakdown:

US Liquid Quart:

* 1 US liquid quart = 946.353 milliliters (mL)

* 1 milliliter (mL) = 1 cubic centimeter (cm³)

* Therefore, 1 US liquid quart = 946.353 cubic centimeters (cm³) or 946,353 cubic millimeters (mm³)

Imperial Quart:

* 1 imperial quart = 1.13652 US liquid quarts

* Therefore, 1 imperial quart = 1,079.964 cubic centimeters (cm³) or 1,079,964 cubic millimeters (mm³)

Important Note: While we can calculate the volume in cubic millimeters, it's less common to use that unit for liquid measurements. It's usually expressed in milliliters (mL) or liters (L).