Hello and welcome to Apple Support Communities, Shamal Anushka.
If I understand your post correctly, you are able to download music from Apple Music but you're unable to play that music unless you're connected to Wi-Fi. Since Wi-Fi is not always available, it's important to be able to listen with or without it. I'd like to help.
First, make sure you're following these steps to download music:
Before you can download content to listen to offline, you need to add it to your Library. Then, in the Music app on your iPhone, iPad, or iPod touch; in iTunes on your Mac or PC; or in the Apple Music app on your Android phone, find the item that you want to download, and follow these steps:
- On your iPhone, iPad, iPod touch, or Android phone: Tap Download
.
- On your Mac or PC: Click Download
.
You'll see
when the download is complete.
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
or
.
Use the Watch app on your iPhone to add music to your Apple Watch.
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, shows, and movies from the Apple Music catalog
If these are the steps you're using and you're still unable to listen unless Wi-Fi is on, let us know if the songs you downloaded are visable under Downloaded Music. Tap Music > Library > Downloaded Music to find out.
Thanks for using the Apple Support Communities. Take care.