A Curious List

I write a list beginning with the number 11. Then, I write all the multiples of 22 until 22{ 2 }^{ 2 }. Next, I write all the multiples of 33 until 32{ 3 }^{ 2 }, and I continue writing numbers successively. The first numbers of the list are 1,2,4,3,6,9,4,8,12,16,5,1, 2, 4, 3, 6, 9, 4, 8, 12, 16, 5,\ldots

Find the sum of the digits of the position number in which 2016 appears for the first time.

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