1 cubic meter has 1000 liters of liquid. Meter is a unit independent of kilogram.

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Then why does 1 liter of water at max density (4 °C) have a mass of 1 kg? Is it a mere coincidence?

It is not a coincidence. As the Wikipedia article on the Litre says:

One litre of water has a mass of almost exactly one kilogram when measured at its maximal density, which occurs at about 4 °C. Similarly: one millilitre (1 mL) of water has a mass of about 1 g; 1,000 litres of water has a mass of about 1,000 kg (1 tonne). This relationship holds because the gram was originally defined as the mass of 1 mL of water; however, this definition was abandoned in 1799 because the density of water changes with temperature and, very slightly, with pressure.

1 liter of water equals $1\ \mathrm{kg}$ weight.1 liter of water is also the same as $1000\ \mathrm{cm^3}$ i.e. cubic centimeter ($10\ \mathrm{cm}\times10\ \mathrm{cm}\times10\ \mathrm{cm}$ in volume) and1 liter is the same as 1 cubic decimeter (10 centimeters is 1 decimeter).

Therefore 1 cubic meter volume is the same as 1000 cubic decimeter or 1000 liters and that is why 1000 liters of water weighs $1000\ \mathrm{kg}$ or 1 ton.Similarly, $1\ \mathrm{cm^3}$ is the same as $1\ \mathrm{ml}$ and weighs $1\ \mathrm g$ of water.

It is not a mere coincidence but a simple equivalence measurement between the Metric system and the SI system of measurements.

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