Java 8 introduces Map.merge(K, V, BiFunction), which makes this easy if not particularly concise:
Map<String, String> result = new HashMap<>(map1);
//or just merge into map1 if mutating it is okay
map2.forEach((k, v) -> result.merge(k, v, (a, b) ->
Integer.toString(Integer.parseInt(a) + Integer.parseInt(b))));
If you're doing this repeatedly, you're going to be parsing and creating a lot of strings. If you're generating the maps one at a time, you're best off maintaining a list of strings and only parsing and summing once.
Map<String, List<String>> deferredSum = new HashMap<>();
//for each map
mapN.forEach((k, v) ->
deferredSum.computeIfAbsent(k, x -> new ArrayList<String>()).add(v));
//when you're done
Map<String, String> result = new HashMap<>();
deferredSum.forEach((k, v) -> result.put(k,
Long.toString(v.stream().mapToInt(Integer::parseInt).sum())));
If this summing is a common operation, consider whether using Integer as your value type makes more sense; you can use Integer::sum
as the merge function in that case, and maintaining lists of deferred sums would no longer be necessary.