You need a new, quality PSU. This is an old, non-quality PSU. Even if it were a quality PSU, you can only use the cables that come with a semi-modular or modular PSU because these cables are not standardized on the PSU's end.
When people use their "own" cables, they're not using generic power cables, they're using aftermarket parts that are specifically configured for the correct pinout of the PSU in question. You'll see lots of (fairly costly) custom cables for people using various EVGA, SeaSonic, Corsair, Antec PSUs and the like. For Ultras...not so much, for the same reason you don't see a lot of aftermarket mod kits for 1988 Yugos.