Ganesha and Karthikeya both are sons of Lord Shiva and Goddess Parvati.
do you Know Devi Parvati didnot give birth to any of her kids from her womb , because she was cursed so by Devi Rati.
Devi Rati, wife of Kamdev, why did she cursed devi Parvati?
Kamdeva the God of Love was sent by devatas to help Devi Parvati in breaking Shiva’s Trans state which he took after sacrifice of Sati. Devi Parvati was incarnation of Devi sati.
Enraged Shiva and shiva burnt Kamadeva into Ashewith his third eye.
Ganesha and Kartikeya on peacock
A story of karthikeya and Ganesha:
Once Ganesha and Karthikeya had a competition to decide which among them is faster so they decided to take a round of the world and see who will return the starting point first. Karthikeya at once sat on his mount Peacock and the Peacock started flying towards the Sky. Ganesha used his wisdom and he took a round around his parents when karthikeya returned, Ganesha told him that his world is his parents and he had completed the round much before.
Ganeha and Kathikeya
Bal Ganesha and Karthikeya