Have you actually tried that? Be advised that it might suck depending on your version. A cube with 12 dimensions returns a mere 4096 rows (discussion is regarding millions). Compare times for 8i, 9.2 and 10g below...
Code:
Oracle8i Enterprise Edition Release 8.1.7.4.0 - Production
JServer Release 8.1.7.4.0 - Production

SQL> SET TIMING ON;
SQL> SELECT COUNT (*)
  2  FROM  (SELECT 1
  3         FROM   dual
  4         GROUP BY CUBE (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1));

  COUNT(*)
----------
      4096

Elapsed: 00:00:00.00
SQL> 

Oracle9i Enterprise Edition Release 9.2.0.5.0 - 64bit Production
With the Partitioning, OLAP and Oracle Data Mining options
JServer Release 9.2.0.5.0 - Production

SQL> SET TIMING ON;
SQL> SELECT COUNT (*)
  2  FROM  (SELECT 1
  3         FROM   dual
  4         GROUP BY CUBE (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1));

  COUNT(*)
----------
      4096

Elapsed: 00:00:52.09
SQL> 

Oracle Database 10g Enterprise Edition Release 10.1.0.2.0 - 64bit Production
With the Partitioning, OLAP and Data Mining options

SQL> SET TIMING ON;
SQL> SELECT COUNT (*)
  2  FROM  (SELECT 1
  3         FROM   dual
  4         GROUP BY CUBE (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1));

  COUNT(*)
----------
      4096

Elapsed: 00:01:34.07
SQL>