4. If a positive integer is equal to 4 times the sum of its digits, then we call this positive integer a quadnumber. The sum of all quadnumbers is $\qquad$ .


4.120.

Case analysis.
There are no four-composite numbers that are single-digit numbers.
For two-digit four-composite numbers, they satisfy
$$
\overline{a b}=4(a+b) \text {. }
$$

Thus, the four-composite numbers can be found to be $12, 24, 36, 48$, and their total sum is 120. For three-digit four-composite numbers, they satisfy
$$
100 a+10 b+c=4 a+4 b+4 c,
$$

which has no solution. This indicates that there are no three-digit four-composite numbers. Similarly, it can be analyzed that there are no four-composite numbers with more than three digits.