In Ramayan Lord Rama and his brothers have sons who is the eldest among these children.
Vālmīki Rāmāyaṇa spends very little time on the sons of Bharata (Takṣa-Puṣkara), Lakṣmaṇa (Aṅgada-Candraketu) and Śatrughna (Subāhu-Śatrughāti). The only place they are mentioned is towards the end of Uttarakāṇḍa when they are established as kings by their respective fathers.
Given this, it's impossible to determine the eldest among all of these.
The lord of Kekaya heard that Bharata had come as the commander. With Gargya, Yudhajit was filled with great delight. With a large crowd of people, Yudhajit emerged. He swiftly advanced against the gandharvas, who were like the gods in their forms. Light in their valour, Bharata and Yudhajit met. With their forces and foot soldiers, they reached the city of the gandharvas. Hearing that Bharata had arrived, the immensely brave gandharvas assembled, desiring to fight. They roared in every direction. A tumultuous battle that made the body hair stand up commenced. It was extremely terrible and continued for seven nights, but neither side could defeat the other. There was an extremely terrible weapon made out of black iron and it was named Samvarta. Enraged, Bharata, Rama’s younger brother, invoked it against the gandharvas. Shattered by Samvarta, they were bound in the nooses of death. In an instant, three crores of great-souled ones were struck. The residents of heaven could not remember a strike which was this terrible. In an instant, those great-souled ones were reduced to this state. Bharata, Kaikeyee’s son, slew those brave ones and populated two excellent and prosperous cities there. Taksha became the king of Takshashila and Pushkara of Pushkaravata. These were two beautiful cities in the land of Gandhara, in the dominion of the gandharvas...
Hearing this, with his brothers, Raghava was delighted. Raghava addressed his brother in these extraordinary words. ‘O Soumitri! These two sons of yours, Angada and Chandraketu, are accomplished in dharma. They are firm in wielding bows and deserve kingdoms. I will consecrate them in virtuous and beautiful kingdoms that are appropriate, without any obstructions. Let these two archers find pleasure there. They should not suffer from any other king there. Nor should the hermitages there be destroyed. O amiable one! Search for such a country, so that we do not commit a crime.’ Thus addressed by Rama, Bharata replied, ‘There is the land of Karapatha. It is beautiful and without any disease. Instate the great-souled Angada in that city. Instate Chandraketu in beautiful Chandrakanta, which is also without disease.’ Raghava accepted the words that Bharata had spoken. He brought that country under his subjugation and instated Angada there. The beautiful city of Angadiya was populated by Angada. It was beautiful and was protected by Rama, who was unblemished in his deeds. Chandraketu populated the Malla kingdom with wrestlers. It was divine, like a city in heaven and became famous by the name of Chandrakanta. Rama, Bharata and Lakshmana were filled with great delight. They consecrated the princes and the two of them left with their forces and followers. Angada occupied the territory towards the west and Chandraketu towards the north. Soumitri followed Angada and Bharata followed Chandraketu, to help them along the flanks. Lakshmana resided in Angadiya for one year. When his invincible son was instated, he returned again to Ayodhya...
Urged by Rama’s words, the messenger, light in his valour, swiftly left for Madhura and did not spend any nights during the journey. He reached Madhura in three days and nights and told Shatrughna everything about what had transpired— the abandonment of Lakshmana, Raghava’s pledge, the consecration of the two sons and the decision of the citizens to follow. The intelligent Rama had created a beautiful city for Kusha to the north of the Vindhya mountains and it was named Kushavati. The beautiful city that was referred to as Shravati was for Lava. Leaving Ayodhya empty, Bharata intended to follow Raghava. He reported all this to the great-souled Shatrughna. The messenger stopped and added, ‘O king! Hurry.’ The news was terrible and the destruction of the lineage was nigh. Hearing this, the descendant of the Raghu lineage summoned the ordinary people and the priest, Kanchana, and told all of them about what had happened. He also said that with his brothers, he too would be destroyed. Therefore, the valiant lord of men instated his two sons. Subahu obtained Madhura and Shatrughati obtained Vaidisha. He divided the forces in Madhura among the two sons. With riches and grain, he established these two kings. He took his leave from the king of Vaidisha, Shatrughati. Alone on a chariot, Raghava left for Ayodhya...
Short Answer: Kusha, the son of Rama is eldest among all.
Long Answer: Shri Rama had twins - Luva and Kusha. Kusha is the elder among two. Following reference can be taken to understand this.
Laxmana also had two sons - Angada and Chandraketu. Similarly Bharata's sons were Taksha and Pushkala. Shatrughana too had two children - Shatrughati and Subahu.
Similar Question have been asked previously, although it was related to the children of Shri Rama only. That's why I didn't flagged this one as a duplicate. Look at https://hinduism.stackexchange.com/a/9542/20695
Throne of Shri Rama was given to Kusha.