These are the relationships of the Earth Ninja Cole.
Is Cole's father and dancer who wanted his son to follow in his footsteps. When Cole was a child, Lou sent him to Marty Oppenheimer School of Performing Arts but Cole ran away from the school and wouldn't see his father for sometime. After reuniting with father, Cole was unable to admit that he ran away from the school and became a ninja. Lou found out and was furious but watched Cole battled the serpentine being impressed with his son's choice. The two reconciled the relationship and have become closer as Lou once made a song to show how proud he was of him. In Day of the Departed, Lou wondered what was taking Cole so long as he was looking forward to lighting lanterns for the holiday. In The Hands of Time, Cole was surprised to find his father held hostage by the Vermillion and with the help of his friends freed him.
Nya and Cole are good friends throughout the series, but in Season 3, Nya developed a crush on Cole, which caused him a rivalry between him and Jay that continues on in Season 4.
In season 5, when Cole became a ghost, she supported Cole to keep on trying with his life and never give up. In Season 6, Nya ultimately chooses to be with Jay but Cole is supportive of her choice with all three remaining good friends in the end.
In Day of the Departed, Nya and the other Ninja are glad Cole was okay and became a human again.
Cole is Wu's student along with the other Ninja. When Cole and the other train to become Ninjas, he is shown to really care about Wu and glad to have him mentoring them.
Like the other Ninja, Wu sees Cole as one of his best students.
Jay and Cole are best friends in the series. They may be annoyed by one and another due to the differing personalities but they always got each other's backs.
In Season 3, when Nya developed a crush on Cole, this makes Jay upset and cause them to be rivals for her affections which along with Zane's "death" to defeat The Overlord serves a reason for the team breaking up.
In season 4, they refuse to be on the same team again and continue fighting with each other about Nya. When Chen forces them to duel in the tournament, the two get out some of their pent-up frustration but in the end they rekindle their friendship with Cole sacrificing himself so Jay could advance. They maintain their friendship in the next seasons with Jay expressing sadness when Cole was turned into a ghost by Yang and attempting to move him out of his despair.
In Day of the Departed, when the ninja rushed to Cole's aid as he was fight Yang, Cole was reenergized and managed to overpower and defeat the ghostly master. When Cole was thought to be departed, Jay broke down and stated he would give anything to have Cole back, which the latter overheard. Jay and other Ninja were relieved when Cole was okay and became a human again.
Like the others, Cole was put off by Zane's personality but when finding out he was nindroid, he and the others supported and accepted their friend.
When Zane sacrificed himself to defeat The Overlord and was seemingly destroyed, Cole was distraught his demise and was unable to continue being a ninja. In season 4, when Lloyd suggested replacing Zane, Cole and the others were adamant about not replacing Zane until they spotted a poster that said he was still alive causing them to enter Chen's fighting tournament to find him. After being eliminated from the tournament, Cole was the first of the ninja to find Zane, being relieved to see him alive and well in a new form and immediately promised to break him out of his captivity. Working together, they manage to break free however, due to Cole's promise of breaking the other elemental masters out of Chen's grasps, he implored Zane to leave while he goes back. To his surprise, Zane decides to help him deeming that ninja never leave one another behind. After a series of plans, they were successful in liberating the captives and join their allies in defeating Chen.
In Day of the Departed, Zane and the others were very happy Cole was fine and became a human again.
They are good friends throughout the series. In Season 5, Kai was sad that Cole became a ghost and attempted to move him out of his sadness.
In Day of the Departed, Kai and the others were very happy to see Cole return to being a human.
Lloyd and Cole are good friends throughout the series. When Lloyd was feeling down in some battles against their enemies, Cole and the other support him and help inspire him. When Lloyd was possessed by Morro, he and the other would do anything to rescue. Cole was glad that Lloyd was saved from Morro's possession.
In Day of the Departed, Lloyd and the other ninja was glad to see that Cole was okay and became a human again.