iPhone 6 Plus is an outdated iPhone (9 september 2014), > 7 years old, which also affects the battery life. That may be the cause of the problem.
It is possible to have the battery replaced, the battery can be replaced by Apple or an Apple Authorized Service Provider.
See this Apple article:
https://support.apple.com/iphone/repair/service/battery-power
If you are going to replace the battery, by Apple or an Apple Authorized Service Providers read this Apple article:
Get your iPhone, iPad, or iPod touch ready for service
Get your iPhone, iPad, or iPod touch ready for service - Apple Support