In what different ways could a large colonial population the economy of the mother country?

 The most obvious way would be manufacture of goods and exporting. Take Canada for example. Canada used to be a French colony with lush forests full of animals to hunt. The french hunted animals for their pelts which would then be taken back to Europe and sold at high prices. Others would sell spices or tea, some would take oil or gold, depending on where the colonies are.

The answer is ethnic groups.