If I cut sugar from my diet, what can I replace the calories with as a substitute?

Eat much fat and protein. Much sugar together with fat is not healthy in long term. Over time it can slow down the blood flow wich easier leads to diseases when you are older. It smart of you to cut sugar from your diet. For example you can eat food like pizza which contains much fat, protein and some carbohydrates.

Whatever you want.  

1. Fats have the highest number of calories, so increasing your fat intake will provide your body with essential fatty acids and calories.  Consider eating avocados, nuts, nut butters, and  cream.

2. Carbs from fruit, grains, beans, etc. will provide calories -- not much nutritional value, but definitely calories.  Carbs are turned into sugar in your body and help you store extra calories as fat. 

4. Protein.  Protein and carbs have the same amount of calories per gram. Eating protein that also contains good fat (think a steak or salmon) is a great way to increase your ability to build muscle and also consume nutrients.

Protein, complex carbs, good fats.

Knowing what you are wanting to achieve would help.

Most people give up sugar to lose weight which you are saying you neither want nor need to do.

If it is that you are wanting to expand the range of foods you eat, this is best done slowly. 

You can eat all the fruit and vegetables you want without risk.

And don't forget to drink plenty of filtered water

Eat real food (i.e. anything that doesn't come in a brightly coloured package or box).