KöMaL 2013 K398

In the six-digit number 135726, the digit in the thousands' place (the 5) is equal to the double of the number of hundred thousands plus the number of ten thousands (that is, $2^.$1+3). The digit in the hundreds' place (the 7) is equal to the double of the number of ten thousands plus the number of hundred thousands (that is, $2^.$3+1). The digit in the tens' place is twice the number of hundred thousands, and the digit in the units' place is twice the number of ten thousands. The number given as an example above is divisible by six. Is it true that all numbers of this property are divisible by six?