In the past, you need modify rtc_api.c in mbed-dev source code. From this revision, you can just use RTC function all of conditions (Normal, Reset, Stand-by, Power OFF).

Note

From now on, you do NOT need any modification for mbed-dev library because STM team updates rtc_api.c source code and support RTC function under reset & standby condition includes power off condition (You need additional VBAT back-up hardware).

Please refer following NOTE information.
/users/kenjiArai/notebook/nucleo-series-rtc-control-under-power-onoff-and-re/

Revision:
5:bc464a588c2e
Parent:
4:a9cebfe4715f
Child:
6:5ada291037aa
--- a/main.cpp	Thu Feb 19 02:59:11 2015 +0000
+++ b/main.cpp	Sat May 23 22:26:37 2015 +0000
@@ -6,7 +6,7 @@
  *  http://www.page.sannet.ne.jp/kenjia/index.html
  *  http://mbed.org/users/kenjiArai/
  *      Created: January   17th, 2015
- *      Revised: Feburary  19th, 2015
+ *      Revised: May       24th, 2015
  *
  * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED,
  * INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE
@@ -26,9 +26,10 @@
 
 #define USE_LCD
 
-#if defined(TARGET_NUCLEO_F401RE) || defined(TARGET_NUCLEO_F411RE) || defined(TARGET_NUCLEO_L152RE)
+#if defined(TARGET_NUCLEO_F401RE) || defined(TARGET_NUCLEO_F411RE) \
+ || defined(TARGET_NUCLEO_L152RE) || defined(TARGET_NUCLEO_F334R8)
 #else
-#error "Target is only Nucleo F401RE, F411RE and L152RE"
+#error "Target is only Nucleo F401RE, F411RE, F334R8 and L152RE"
 #endif
 
 //  Object ----------------------------------------------------------------------------------------
@@ -69,7 +70,7 @@
 #endif
     pc.printf("\r\n\r\nTest Nucleo RTC Function\r\n");
     myled = !myled;
-    if (SetRTC() == 1) {
+    if (SetRTC(0) == 1) {
         pc.printf("External");
         xtal = 1;
     } else {