Is it a coincidence that 1 liter water has a mass of 1 kg while 1 cubic meter has 1000 liters of water?

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

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) and 1 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.

• Welcome to stack exchange. Unfortunately, your math does not answer the question "why this relationship hold". – Semoi Dec 18 '19 at 20:52
• "It is not a mere coincidence but a simple equivalence measurement between the Metric system and the SI system of measurements." Isn't the equivalence between metric and SI more due to the fact that SI is directly based off metric units? – JMac Mar 19 '20 at 14:51