You supply 400 kilocalories of heat energy to a block of ice, with a mass of 14 kg. What will be the outcome?

It takes 80 calories to melt 1 g of ice. So you have 400,000 calories.

400,000/80 = 5,000.
So 5,000 grams of ice will melt and you should end up with 5000 g liquid water and 9,000 g un-melted ice all at zero C.