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Because in your particular case copyMakeBorder makes extrapolation, as a result you have got slightly different sum value. To prevent this you can make custom copy without extrapolation:

cv::Mat computeDFT(cv::Mat image, int optimal_rows, int optimal_cols) {
    cv::Mat padded = cv::Mat(optimal_rows, optimal_cols, image.type());

    std::cout << image.rows << " " << image.cols << " " << image.type() << " " << cv::sum(image) << std::endl;

    cv::Mat _tempmat = cv::Mat(padded, cv::Rect(0,0,image.rows,image.cols));
    image.copyTo(_tempmat); 

    std::cout << padded.rows << " " << padded.cols << " " << padded.type() << " " << cv::sum(padded) << std::endl;


    cv::Mat complexImage(padded.rows, padded.cols, CV_64FC2);
    cv::dft(padded, complexImage, CV_HAL_DFT_COMPLEX_OUTPUT);
    return complexImage;
}

Because in your particular case copyMakeBorder makes extrapolation, as a result you have got slightly different sum value. To prevent this you can make custom copy without extrapolation:

cv::Mat computeDFT(cv::Mat image, int optimal_rows, int optimal_cols) {
    cv::Mat padded = cv::Mat(optimal_rows, optimal_cols, image.type());

    std::cout << image.rows << " " << image.cols << " " << image.type() << " " << cv::sum(image) << std::endl;

    cv::Mat _tempmat = cv::Mat(padded, cv::Rect(0,0,image.rows,image.cols));
cv::Rect(0,0,image.cols,image.rows));
    image.copyTo(_tempmat); 

    std::cout << padded.rows << " " << padded.cols << " " << padded.type() << " " << cv::sum(padded) << std::endl;


    cv::Mat complexImage(padded.rows, padded.cols, CV_64FC2);
    cv::dft(padded, complexImage, CV_HAL_DFT_COMPLEX_OUTPUT);
    return complexImage;
}