Having the withCredentials key enabled (set to 'true') should solve your issue.

Please try this:

const
    fs = require('fs'),
    https = require('https'),
    axios = require('axios');

function reqTest()
{

    axios.default.request({
        'url': 'google.com',
        'method': 'post',
        'headers':
            {
                'Cookie': 'cookie1=?; cookie2=?;'
            },
        'withCredentials: true" // ADD THIS LINE
    }
    ).then(res => {
        console.log(res);
    })
}

You can also enable this property for all requests in this instance of axios, changing axios' defaults:

axios.defaults.withCredentials = true;

axios.post(url, body).then(...).catch(...); // withCredentials is automatically enabled

Please report results.