Nutritional needs for infants, like adults, vary depending on some variables. Body composition and weight are going to cause the exact numbers of calories per day and protein per day to change. Low weight, early births are also going to bring in some additional factors, so the following information is recommended nutritional numbers for "normal" infants.
There are six nutrients that the body needs: water, vitamins, minerals, proteins, fats, and carbohydrates. The proteins, fats, and carbohydrates are the nutrients that contribute to the caloric intake of a person. In general, carbohydrates should make up about 55%–60% of an adult's daily caloric intake. 12%-20% should come from proteins, and the rest should be fat. In an adult, this means that about .8 grams per kilogram per day of protein should be consumed; therefore, an 82 kilogram adult should consume about 65 grams of protein.
Infant caloric and protein needs are slightly different. The USDA recommends 9.1 grams of protein per day for children 0–6 months of age. That number increases to 11 grams per day for children 7–12 months of age. This translates to about 1 gram per kilogram per day. The recommended total daily caloric intake of children under a year of age does vary, but it doesn't vary that much. 0–2 month old children should be consuming about 100–120 kcal/kg/day. That number drops to 95 kcal/kg/day for 3 month old children, and it drops to 82 kcal/kg/day for 4–12 month old children. Coming up with these kinds of exact calorie needs per kilogram for you (as the question indicates) is much harder because the caloric intake need of an adult is going to be hugely influenced by activity levels. Using myself as an example, my caloric needs are higher than an average adult because I run 5–6 miles per day.