Given that you are storing a list of numbers in a delimited string field, "24; 35; 67", you have exactly two options. One is iteration (a loop); the other is recursion. You do not have the option of using aggregate queries or roll-up summary fields because you don't have actual number fields to look at.
Apex does not natively support a
reduce() function, a list comprehension, or another such construct with which you may be familiar from other languages. Any such construct implemented in Apex will just be a facade over iteration or recursion.
Iteration is the natural approach here and should be used, barring changes to the data model. If you have broader needs that aren't articulated here, you may consider adding a child object to store an actual number field in a one-to-many relationship, which you can then address using SOQL aggregate queries and roll-up summary fields.