e62.scala

@annotation.tailrec
def findTheCubedNum(num: BigInt, cache: Map[String, List[BigInt]]): BigInt = {
  val cubed = num.pow(3)
  val key   = cubed.toString.sortWith(_ < _)
  val nums  = cubed :: cache.getOrElse(key, List[BigInt]())
  if (nums.length == 5) return nums.min
  findTheCubedNum(num + 1, cache.updated(key, nums))
}

val answer = findTheCubedNum( BigInt(1), Map[String, List[BigInt]]() )
println(answer) // => 127035954683