I've read lot of similar questions but did not find acceptable answer for me.
I'm writing simple drive uploading tasks for gradle to upload android .apk file after a successful build. I don't use Drive Java API, just REST requests.
This task retrieves token:
task getToken << {
  def keyStoreFile = file("SomeProject-PrivateKey.p12")
  def keyStorePass = "notasecret"
  def serviceAccountEmail = "someserviceemail@someproject.iam.gserviceaccount.com"
  def keyStore = java.security.KeyStore.getInstance("PKCS12")
  keyStore.load(keyStoreFile.newInputStream(), keyStorePass.toCharArray())
  def privateKey = keyStore.getKey(keyStore.aliases().nextElement(), keyStorePass.toCharArray())
  def JWTHeader = '{"alg":"RS256","typ":"JWT"}'
  def JWTClaimSet = '{\n' +
        '  "iss":' + serviceAccountEmail + ',\n' +
        '  "scope":"https://www.googleapis.com/auth/drive",\n' +
        '  "aud":"https://www.googleapis.com/oauth2/v4/token",\n' +
        '  "exp":' + (System.currentTimeSeconds() + 5 * 60) + ',\n' +   // + 5 minutes
        '  "iat":' + System.currentTimeSeconds() + '\n' +
        '}'
  def JWT = new String(Base64.urlEncoder.encode(JWTHeader.bytes)) +
        '.' + new String(Base64.urlEncoder.encode(JWTClaimSet.bytes))
  def signature = java.security.Signature.getInstance("SHA256withRSA")
  signature.initSign(privateKey)
  signature.update(JWT.bytes)
  JWT += '.' + new String(Base64.urlEncoder.encode(signature.sign()))
  System.out.print "assertion: " + JWT + "\n"
  def authUrl = new URL("https://www.googleapis.com/oauth2/v4/token")
  HttpURLConnection auth = authUrl.openConnection()
  auth.setRequestMethod("POST")
  auth.setRequestProperty("Host", "www.googleapis.com")
  auth.setRequestProperty("Content-Type", "application/x-www-form-urlencoded")
  auth.setDoOutput(true)
  def body = 'grant_type=urn%3Aietf%3Aparams%3Aoauth%3Agrant-type%3Ajwt-bearer' +
        '&assertion=' + JWT
  auth.outputStream.write(body.bytes)
  def reader = new BufferedReader(new InputStreamReader(auth.inputStream))
  StringBuilder sb = new StringBuilder()
  for (int c; (c = reader.read()) >= 0;)
    sb.append((char) c)
  System.out.println(sb.toString())
}
And this one upload file to some public folder or folder shared with serviceemail@someproject.iam.gserviceaccount.com:
task uploadToDrive << {
  File apk = file("test1.txt")
  //    File apk = file("test2.apk")
  def url = new URL("https://www.googleapis.com/upload/drive/v3/files?uploadType=multipart");
  HttpURLConnection drive = url.openConnection();
  drive.setRequestMethod("POST")
  drive.setRequestProperty("Host", "www.googleapis.com")
  drive.setRequestProperty("Authorization", "Bearer " + "ya29.ElnDA_idxn6dL4cji6Oh3dQbdCaMGtGfmIMwIDa4yrEgiL9G8I6qHeSoCNUwcfYESZiLBBaymYLWJQBuTgypqyOy_YVUNpwyd2Gf8rYLgAsSksNnruygoFBS9g")
  drive.setRequestProperty("Content-Type", "multipart/related; boundary=foo_bar_baz")
  String body = '\n' +
        '--foo_bar_baz\n' +
        'Content-Type: application/json; charset=UTF-8\n\n' +
        '{\n' +
        '  "name": "TEST",\n' +
        '  "parents": [ "0BzkpQECQo2d2SEo5OTd4RHpnOFE" ]\n' +
        '}\n\n' +
        '--foo_bar_baz\n' +
        'Content-Type: application/octet-stream\n\n'
  String end = '--foo_bar_baz--'
  drive.setFixedLengthStreamingMode(body.bytes.length + apk.length() + end.bytes.length)     // Content Length
  drive.setDoOutput(true)
  drive.setDoInput(true)
  drive.outputStream.write(body.bytes)
  apk.withInputStream { is ->
    def buffer = new byte[1024];
    int len;
    while ((len = is.read(buffer)) != -1) {
        drive.outputStream.write(buffer, 0, len);
    }
  }
  drive.outputStream.write(end.bytes)
  def reader = new BufferedReader(new InputStreamReader(drive.inputStream))
  StringBuilder sb = new StringBuilder()
  for (int c; (c = reader.read()) >= 0;)
    sb.append((char) c);
  System.out.println(sb.toString())
}
For small files it works well! But when I try to upload real .apk file or even ~1Mb image gradle fails:
Execution failed for task ':uploadToDrive'. Server returned HTTP response code: 400 for URL: https://www.googleapis.com/upload/drive/v3/files?uploadType=multipart
Any ideas?