One approach is using std::accumulate like this:
#include <numeric>
const int result = std::accumulate(f_table[1].cbegin(), f_table[1].cend(),
0, [](int result, const auto& entry){ return result + entry.second; });
Note that as @StoryTeller pointed out in the comments, you might want to prefer a parallel version of this algorithm, which will ship with fully conforming C++17 implementations, i.e., std::reduce.
Another option is a range based for loop. With structured bindings (again available in C++17), you might consider this more readable:
int result = 0;
for (const auto& [key, value] : f_table[1])
result += value;
And finally a solution based on range-v3:
#include <range/v3/all.hpp>
using ranges::view::values;
using ranges::accumulate;
const int result = accumulate(f_table[1] | values, 0);
std::array<std::array<int, 3>, 3>and zero-index?std::unordered_map? When you know that it should become easy.