Using Elixir of Brilliance during the mid and late game is a good way to reach the 40% cooldown reduction cap without having to buy extra items.
Elixirs are often bought towards the end of long games when builds are all completed and the extra gold continues to accumulate. They can also be bought mid game to give a temporary stat advantage during ganks and teamfights, or even at level one.
Consuming this item along with Elixir of Fortitude will cause the colored auras to alternate from blue and red.
Elixirs are automatically applied when purchased if there are already 6 items in the inventory.