Which would require more energy heating an ideal gas at constant pressure or at constant volume why

If you cannot understand, you are not alone; even teachers find difficulty to grab. The difficulty of understanding is due to the rubbish ways of explanation in academic/ textbook. Let's see the actual concept. Cv is heat capacity at constant volume. Constant volume has no direct meaning in heat retaining capacity. Constant volume indirectly means work done is prevented. In this situation, all the heat, if added, is contained within the system volume.

On the other case, Cp is heat capacity at constant pressure. Constant Pressure is of no meaning in heat containing capacity. But the fact is: when heat is added, system pressure raises leading to expansion. During expansion, some of energy is expelled i.e. transported to boundary/ periphery and resides over the boundary as potential energy between the system and neighbour/ surrounding. Here, heat is kept in two locations - one) within volume, two) Over-periphery.

While Cv is referring capacity within volume, Cp is referring capacity within volume as well as on periphery. Hence Cp is more than Cv. Cv may be redefined as heat capacity within volume and Cp may be redefined as heat capacity within upto periphery.