3. A natural number greater than 0, if the sum of all its divisors equals twice itself, is called a perfect number or a complete number. For example, the divisors of 6 are $1,2,3,6,1+2+3+6=12$, so 6 is the smallest perfect number. The question of whether there are infinitely many perfect numbers remains one of the challenges that have puzzled humanity. Research on perfect numbers can begin with calculating the sum of all divisors of a natural number. The sum of all divisors of 8128 is $\qquad$.
Analysis:
Prime factorization: $8128=2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 127=2^{6} \times 127$;
Sum of divisors: $\left(2^{0}+2^{1}+2^{2}+2^{3}+2^{4}+2^{5}+2^{6}\right) \times\left(127^{0}+127^{1}\right)=(1+2+4+8+16+32+64) \times(1+127)=16256$.