a music downloading problem

Yes, just import those songs into the itunes library and tell itunes to sync these songs.

iTunes can automatically scan for music files. To scan:

1.Open iTunes.

2.Select the Music icon in the upper-left corner.

3.Click My Music from the upper-middle.

4.Click "Scan for Media."

or you can manually add the music from a folder on your computer:

1.Open iTunes.

2.Choose File > Add Folder to Library. If you do not see the File, Edit or View options, press Ctrl and B together on your keyboard.

3.Locate the folder on your computer that contains the music you wish to import into iTunes.

4.Once you select your folder you should now see your newly imported files in your iTunes library.