something like that sould do it bute force: - although there is a nice analytic solution (think pen& paper) using mathematics - that may also work for numbers greater than 1000.
final String bignumber = BigInteger.valueOf(2).pow(1000).toString(10);
long result = 0;
for (int i = 0; i < bignumber.length(); i++) {
result += Integer.valueOf(String.valueOf(bignumber.charAt(i)));
}
System.out.println("result: " + result);