To convert liters to milliliters, you multiply the number of liters by 1000, because there are 1000 milliliters in one liter.
For the world record hot chocolate cup:
\[ 3,331 \, \text{L} \times 1000 \, \text{ml/L} = 3,331,000 \, \text{ml} \]
So, the world record for the largest cup of hot chocolate, 3,331 liters, is equal to \( 3,331,000 \) milliliters.