Spartan Cores are one of the many collectibles that Halo Infinite has to offer. These are perhaps the most vital of all the collectibles because they are needed to upgrade your gear. They are scattered all over the map. The Tower has two that you can find. Here is where you can find them.
The Tower is located on the western side of the map. When you take the Pelican to this area after the third mission, head northwest to find The Tower. It will also get marked on your map. If you need help finding its location, check the map above.
When you get inside The Tower, you will need to deal with a lot of enemies. Take them all out before proceeding. The first of the Spartan Cores can be found under the walkway on the right side of The Tower. You will get a quest marker on the walkway when you are activating the gravity lift. Go under the catwalk to find two crates that you can walk inside. The Spartan Core is in the one on the right.
The second Spartan Core can be found inside The Tower. You will need to activate the gravity lift to enter the main structure. Once you are inside, go up to the third floor. When you reach the third floor, make a left and follow the path. The Spartan Core will be toward the middle of the floor hidden in a dark corner.