Does specific heat also mean the amount of energy needed for cooling, or is it only energy for heating?

yes it does

here is a more clearer explanation

Explanation:

The specific heat capacity of water is 4,200 Joules per kilogram per degree Celsius (J/kg°C). This means that it takes 4,200 J to raise the temperature of 1 kg of water by 1°C.

Some other examples of specific heat capacities are:

Material Specific heat capacity (J/kg/°C)

Brick 840

Copper 385

Lead 129

Lead will warm up and cool down fastest because it doesn't take much energy to change its temperature. Brick will take much longer to heat up and cool down. This is why bricks are sometimes used in storage heaters as they stay warm for a long time. Most heaters are filled with oil (1,800 J/kg°C) or water (4,200 J/kg°C) as these emit a lot of energy as they cool down and, therefore, stay warm for a long time.

The specific heat capacity of a material is the energy required to raise one kilogram (kg) of the material by one degree Celsius (°C).

Yes it also means the amount of energy needed for cooling