Hello and welcome to Apple Support Communities, MyloXyloto90.
If I understand your post correctly, you can play songs on Apple Music but you're not able to download songs to listen offline. Since an internet connection is not always available, being able to download songs is important. I'd like to help.
First, make sure you have enough storage available on your iPhone to download songs. This guide will show you how to check:
How to check the storage on your iPhone, iPad, and iPod touch
Then follow these steps to download:
You can download content from the Apple Music catalog or from your iCloud Music Library. If the content is not already in your Library, you must add it before you can download it.
To download an item, find it in your Library and look for
near it. Tap or click
to download the item to your device. On your iOS device, when you download an entire album or playlist,
changes to
DOWNLOADED when the download is complete.
Use the Watch app on your iPhone to add music to your Apple Watch.
If you have Automatic Downloads turned on, content automatically downloads to your device or computer when you add it to your Library. You won't see
.
You can download content on up to 10 devices. This content is accessible only when your Apple Music subscription is active.
See the full article here:
Add and download music and video content from the Apple Music catalog
If you still can't download songs, try using a different Wi-Fi network.
Let us know if that resolves this issue for you.
Thanks for using the Apple Support Communities. Take care.