downloadFiles.java

private void downloadFiles() {
        new Thread(new Runnable() {
            @Override
            public void run() {
                try {
                    if (mAccessToken == null) {
                        Log.d(TAG, "need to sign in first");
                        return;
                    }
                    if (fileSearched == null) {
                        Log.d(TAG, "query file first");
                        return;
                    }

                    Drive drive = buildDrive();
                    File fileToDownload = new File();
                    Drive.Files.Get request = drive.files().get(fileSearched.getId());
                    fileToDownload.setFileName(fileSearched.getFileName())
                            .setId(fileSearched.getId());

                    MediaHttpDownloader downloader = request.getMediaHttpDownloader();
                    downloader.setContentRange(0, fileSearched.getSize() - 1);

                    String path = getExternalFilesDir(null).getAbsolutePath() + "/" + fileSearched.getFileName();
                    request.executeContentAndDownloadTo(new FileOutputStream(new java.io.File(path)));

                    Log.d(TAG, "download success");
                } catch (Exception e) {
                    Log.d(TAG, "download error " + e.toString());
                }
            }
        }).start();
    }