14.27. Given 6 digits: $0,1,2,3,4,5$. Find the sum of all four-digit even numbers that can be written using these digits (the same digit can be repeated in a number).
14.27. Answer: 1769580. We will separately calculate the sum of thousands, hundreds, tens, and units for the considered numbers. The first digit can be any of the five digits $1,2,3,4,5$. The number of all numbers with a fixed first digit is $6 \cdot 6 \cdot 3=108$, since the second and third places can be any of the six digits, and the fourth place can be any of the three digits $0,2,4$ (we are considering only even numbers). Therefore, the sum of thousands is $(1+2+3+4+5) \cdot 108 \cdot 1000=1620000$. The number of numbers with a fixed second digit is $5 \cdot 6 \cdot 3=90$ (the first place can be any of the five digits). Therefore, the sum of hundreds is $(1+2+3+4+5) \cdot 90 \cdot 100=135000$. Similarly, the sum of tens is $(1+2+3+4+5) \cdot 90 \cdot 10=13500$, and the sum of units is $(2+4) \cdot 5 \cdot 6 \cdot 6=1080$.