#include <string>
#include <iostream>
#include <vector>

std::string to_base64(const std::string input)
{
        static const char *BASE64 = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";

        const size_t len = input.length();
        std::string output;

        output.reserve((len + 2) / 3 * 4);

        unsigned remainder = 0;
        unsigned char leftover = 0;

        for (std::string::const_iterator i = input.begin(); i != input.end(); ++i) {
                unsigned char c = *i;
                switch (remainder) {
                case 0:
                        output += BASE64[c >> 2];
                        leftover = c << 6;
                        break;
                case 1:
                        output += BASE64[(leftover >> 2) + (c >> 4)];
                        leftover = c << 4;
                        break;
                case 2:
                        output += BASE64[(leftover >> 2) + (c >> 6)];
                        output += BASE64[c & 0x3F];
                        break;
                }
                remainder = (remainder + 1) % 3;
        }

        switch (remainder) {
        case 1:
                output += BASE64[leftover >> 2];
                output += '=';
                output += '=';
                break;
        case 2:
                output += BASE64[leftover >> 2];
                output += '=';
                break;
        }

        return output;
}

int main()
{

 std::string str = "";
 std::vector<int> vText = {101,20,205,100};   //Вашего синтаксиса мой компилятор не понимает...
 for (size_t i = 0; i < vText.size(); i++)
 {
   str.push_back(char(vText[i]));
 }

 std::cout << to_base64(str); // ZRTNZA==
}