Android Studio 3.1.3 Gradle Sync Error. Could Not Download Gradle-Core.jar

Try to put google() as the first repo as below. Don't put it under jcenter() and mavenCentral() for your existing Android Studio projects.

repositories {
    google() // make this repo as the first one if Android Gradle Plugin is upgraded from 2.x to 3.x. 
    jcenter()
    mavenCentral()
}

For those React Native or CordovaLib projects that are with Android Gradle Plugin lower versions, e.g. 2.2.3, you can try to replace the google() with below, but remember to put it as the first repo selection.

repositories {
    // google()
    maven {
        url "https://maven.google.com"
    }
    jcenter()
}

Clean up all your old .gradle caches and then perform a new Sync.

In my case, for gradle:2.2.3

allprojects {
    repositories {
        maven { url 'https://maven.google.com' }  // now here
        mavenLocal()
        jcenter()
        maven { url "$rootDir/../node_modules/react-native/android" }
        maven { url 'https://maven.google.com' }  // was here
    }
}

hope helpful : )