接口:

http://cdn.banmi.com/banmiapp/apk/banmi_330.apk

简单布局：

<LinearLayout
    android:orientation="vertical"
    xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:app="http://schemas.android.com/apk/res-auto"
    xmlns:tools="http://schemas.android.com/tools"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    tools:context=".MainActivity">

    <Button
        android:id="@+id/bt"
        android:layout_width="match_parent"
        android:layout_height="wrap_content" />

    <TextView
        android:id="@+id/tv"
        android:layout_width="match_parent"
        android:layout_height="wrap_content" />

    <ProgressBar
        android:id="@+id/pb"
        style="?android:progressBarStyleHorizontal"
        android:layout_width="match_parent"
        android:layout_height="wrap_content" />

</LinearLayout>

这里使用OkHttp进行下载
代码：
第一步权限：

  private void initData() {
         if (ContextCompat.checkSelfPermission(this, Manifest.permission.WRITE_EXTERNAL_STORAGE)==
                         PackageManager.PERMISSION_GRANTED){
                     initData1();
                 }else {
                     ActivityCompat.requestPermissions(this,new String[]{Manifest.permission.WRITE_EXTERNAL_STORAGE},
                             100);
                 }
    }

    private void initData1() {
        if (Environment.getExternalStorageState().equals(Environment.MEDIA_MOUNTED)){
            file = Environment.getExternalStorageDirectory();
        }
    }

第二布判断：

 @Override
    public void onRequestPermissionsResult(int requestCode, @NonNull String[] permissions, @NonNull int[] grantResults) {
        super.onRequestPermissionsResult(requestCode, permissions, grantResults);
        if (requestCode==100&&grantResults.length>0&&grantResults[0]==PackageManager.PERMISSION_GRANTED){
            initData1();
        }
    }

第三步解析：

 private void initXia() {
        OkHttpClient build = new OkHttpClient.Builder().build();
        Request build1 = new Request.Builder()
                .url("http://cdn.banmi.com/banmiapp/apk/banmi_330.apk")
                .get()
                .build();
        Call call = build.newCall(build1);
        call.enqueue(new Callback() {
            @Override
            public void onFailure(Call call, IOException e) {

            }

            @Override
            public void onResponse(Call call, Response response) throws IOException {
                ResponseBody body = response.body();
                InputStream inputStream = body.byteStream();
                long l = body.contentLength();
                initStr(inputStream,file+"/b.apk",l);
            }
        });
    }

    private void initStr(InputStream inputStream, String s, long l) {
        try {
            FileOutputStream outputStream = new FileOutputStream(s);
            byte[] arr=new byte[1024*10];
            int a=0;
            while ((a=inputStream.read(arr))!=-1){

                outputStream.write(arr,0,a);
            }
            inputStream.close();
            outputStream.close();
        } catch (FileNotFoundException e) {


        } catch (IOException e) {
            e.printStackTrace();
        }
    }

完整代码：

public class MainActivity extends AppCompatActivity implements View.OnClickListener {

    private Button bt;
    private TextView tv;
    private ProgressBar pb;
    private File file;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);
        initData();
        initView();


    }

    private void initData() {
         if (ContextCompat.checkSelfPermission(this, Manifest.permission.WRITE_EXTERNAL_STORAGE)==
                         PackageManager.PERMISSION_GRANTED){
                     initData1();
                 }else {
                     ActivityCompat.requestPermissions(this,new String[]{Manifest.permission.WRITE_EXTERNAL_STORAGE},
                             100);
                 }
    }

    private void initData1() {
        if (Environment.getExternalStorageState().equals(Environment.MEDIA_MOUNTED)){
            file = Environment.getExternalStorageDirectory();
        }
    }

    @Override
    public void onRequestPermissionsResult(int requestCode, @NonNull String[] permissions, @NonNull int[] grantResults) {
        super.onRequestPermissionsResult(requestCode, permissions, grantResults);
        if (requestCode==100&&grantResults.length>0&&grantResults[0]==PackageManager.PERMISSION_GRANTED){
            initData1();
        }
    }

    private void initView() {
        bt = (Button) findViewById(R.id.bt);
        tv = (TextView) findViewById(R.id.tv);
        pb = (ProgressBar) findViewById(R.id.pb);

        bt.setOnClickListener(this);
    }

    @Override
    public void onClick(View v) {
        switch (v.getId()) {
            case R.id.bt:
                initXia();
                break;
        }
    }

    private void initXia() {
        OkHttpClient build = new OkHttpClient.Builder().build();
        Request build1 = new Request.Builder()
                .url("http://cdn.banmi.com/banmiapp/apk/banmi_330.apk")
                .get()
                .build();
        Call call = build.newCall(build1);
        call.enqueue(new Callback() {
            @Override
            public void onFailure(Call call, IOException e) {

            }

            @Override
            public void onResponse(Call call, Response response) throws IOException {
                ResponseBody body = response.body();
                InputStream inputStream = body.byteStream();
                long l = body.contentLength();
                initStr(inputStream,file+"/b.apk",l);
            }
        });
    }

    private void initStr(InputStream inputStream, String s, long l) {
        try {
            FileOutputStream outputStream = new FileOutputStream(s);
            byte[] arr=new byte[1024*10];
            int a=0;
            while ((a=inputStream.read(arr))!=-1){

                outputStream.write(arr,0,a);
            }
            inputStream.close();
            outputStream.close();
        } catch (FileNotFoundException e) {


        } catch (IOException e) {
            e.printStackTrace();
        }
    }
}