Your i Tunes should be authorized with the Apple ID the songs are bought.
In case you're not sure, connect your i Phone to your PC/MAC, press "Back-up i Phone" (in the summary page of your i Phone) in i Tunes.
Using "account" tab, "authorizing", you can verify your PC and then all purchased music downloaded. I had bought Songs off of Drake's new album which has explicit content.
And for some reason explicit content was turned off on my iphone for music. Check if your music has the [ E ] sign next to it on the store and if so check to see if the explicit content is set to allow on your device.
Connect your i Phone to computer and launch i Tunes.2.
Click the device icon at the top of left of the i Tunes window.3. Connect your i Phone to computer and select "Trust this computer" if you see the pop-up.3. Why not use an i Tunes alternative tool to transfer music to your i Phone, i Pod or i Pad?
A menu should pop up, at the bottom of which you’ll find the “Show Music Available Offline” toggle.
I had this exact same problem and found the answer I was looking for within one of the Apple communities.
Some people say that the music sync sticks with messages like "Waiting to copy items" or "Waiting for changes to be applied." No matter how many times they have tried, no a song has been ever transferred.
Click on there and you will see a list of all songs/albums and you can choose to either download all or individual tracks.
Once downloaded they appear in your library as normal.
Please also check out This Official Apple Page, as it's filled with 54 pages of this same problem.
Are there any music which you didn't purchase using your current Apple ID?