Well Energy itself doesn't have mass per se , but as the first link points out, it is possible under certain circumstances to interconvert mass and energy. That's where E=mc^2 comes in.
When the US was testing out its atom bombs in WW2, they showed that some mass was lost, and transformed into energy (just a little, not all the energy of the bomb). They did the calculations and the data fit E=mc^2 rather well
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