How do I convert a String to a BigInteger?

Using the constructor

BigInteger(String val)

Translates the decimal String representation of a BigInteger into a BigInteger.

Javadoc

According to the documentation:

BigInteger(String val)

Translates the decimal String representation of a BigInteger into a BigInteger.

It means that you can use a String to initialize a BigInteger object, as shown in the following snippet:

sum = sum.add(new BigInteger(newNumber));

BigInteger has a constructor where you can pass string as an argument.

try below,

private void sum(String newNumber) {
    // BigInteger is immutable, reassign the variable:
    this.sum = this.sum.add(new BigInteger(newNumber));
}