Most HR-based estimates of caloric expenditure are on the high side, often up to 100% over. I weigh about 165 and my cals/mile range from 35 to 45 Cals/mile based on powermeter estimates which are generally more accurate than HR. If you're relatively new to cycling you'd probably be on the lower end of that range.

The short answer is yes you need to eat additional food equivalent to what you are burning to maintain your weight. The issue is determining how much you are burning while riding. If you don't want to change your weight I would just eat when you're hungry and monitor your weight over time and adjust you eating as required.