Magitek Core

Magitek Core is a treasure.

Source
Magitek Cores can be obtained as an enemy drop from the following creatures:
 * MA-X DUX - 100% chance
 * MA-X Patria - 3% chance

It can also be obtained as a collectible throughout the world:
 * Gralea
 * Insomnia

It can also be obtained as a sidequest reward from Stealing the Past.

Quests
Magitek Cores are needed for the quest A Better Drillbreaker to upgrade from a Drillbreaker to a Drillbreaker Plus.