Most 600 watt PSU's will have both a 6 pin and an 8 pin PCIe power cable or two 8 pin connectors. Dirty little secret: even if the PSU has two 6 pin connectors, don't worry. Just use them. A 6 pin connector has 3 hot wires (yellow 12 volt lines) and 3 black ground lines. An 8 pin connector has 3 hot wires and 5 ground wires. That means that it cannot carry more current than the 6 pin cable.
Warning: you shouldn't be able to interchange the CPU power and PCIe power cables. (But it's been known to happen.) If you do, you will short 12 volts directly to ground.
For a single Radeon HD 6970 graphics card system AMD recommends a 550 Watt or greater power supply unit with a minimum combined +12 Volt rail current rating of 42 Amps or greater and with at least one 8-pin PCI Express supplementary power connector and one 6-pin PCI Express supplementary power connector.
It is more important to meet the minimum combined +12 Volt rail current rating requirement than the power supply's wattage requirement.
There are very few 550 Watt and 600 Watt power supplies that have 42 Amps or greater on their combined +12 Volt rails.
It's easier to find 620 Watt or 650 Watt power supplies that meet the requirement.