Why implicit conversion doesn't work in Lists?

Could someone give a quick explanation why implicit conversion doesn't work in these cases? Thanks.

scala> implicit def strTwoInt (s: String):Int = s.toCharArray.map{_.asDigit}.sum
strTwoInt: (s: String)Int

scala> List[Int]("1","2","3") sum
res3: Int = 6

scala> List("1","2","3") sum
<console>:9: error: could not find implicit value for parameter num: Numeric[java.lang.String]
        List("1","2","3") sum

scala> val a = List("1","2","3")                          
scala> a.foldLeft(0)((i:Int, j:Int) => i+j)
<console>:10: error: type mismatch;
 found   : (Int, Int) => Int
 required: (Int, java.lang.String) => Int