Adin's eldest son was the only monarch after his father and before his decendent, King Lief, who had more than one child, and the last before Lief to always wear the Belt of Deltora. However, history was somehow obscured and the story of Ballum hidden.
↑ On why Adin's heir is assumed to be male: First, it must be established that the Deltoran monarchy is an absolute progeniture, meaning the eldest in Adin's line always takes the throne, regardless of gender. In The Shadowlands it is revealed that Marilen is "a descendant of Adin's second son" and that she is "next in line to the Belt of Deltora." And although Marilen is technically not the next in line, as that right would go to Bede, according to The Sister of the South, who is a descendant of the brother of King Elstred (Adin's grandson), Ballum, whose history was obscured by Elstred's advisor, Agra, not knowing Ballum's story, Lief believed Marilen to be the next in line. Lief traced the bloodline of Adin's second son, and found Marilen, and it was specified in The Shadowlands that he and Doom never had time to trace anymore than that line. It would stand to reason that they traced the second child's line, as they would be looking for the next in line, not just any heir, at the beginning - though they find many more heirs with time, as revealed by Lief at the end of The Shadowlands. It would stand to reason, then, that Adin's first son is also his first child. It is also highly unlikely that Emily Rodda would overcomplicate things, so the most likely explanation is that Adin's eldest child was a son.
↑ In the first part of The Forests of Silence, the "prologue" titled Part 1: The Belt of Deltora, Jarred finds a book titled The Belt of Deltora in the palace library, detailing the history and the powers of the magic Belt of Deltora. In the text it is said that "The first to leave the belt aside was Adin’s grandson, King Elstred, who in his middle years grew fat with good living and found the steel cut sadly into his belly." This would mean that Adin's eldest son followed his father's ways and always wore the Belt.