If you know the specific heat capacity of a typical brick and the mass of that brick, you can easily calculate its heat capacity. Note that heat capacity depends only on an object's mass and the specific heat capacity of the material.
Definitions

The heat capacity of an object is the amount of heat required to change the temperature of the entire object by 1 degree. Specific heat capacity, the usual quantity given for materials, is the amount of heat required to change the temperature of 1 gram of the material by 1 degree.
Brick

The specific heat capacity of common brick is 0.9 kJ/kg K (kiloJoules per kilogram Kelvin), or in other units, 0.22 kcal/kg K (kilocalories per kilogram Kelvin). This must be converted to heat capacity for a given brick size.
Heat Capacity

To convert from specific heat capacity to heat capacity, multiply specific heat capacity by the mass of the object (since specific heat capacity is heat capacity per unit mass). Assuming that the mass of a typical brick is 2.268 kilograms, the brick's heat capacity is 2.0412 kJ/K (kiloJoules per Kelvin). (The calculation is: 0.9 kJ/kg K multiplied by 2.268 kilograms equals 2.0412kJ/K.)
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 Photo Credit Brick image by Luke Haverkamp from Fotolia.com