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In fact gluons have a QCD charge, they just don't have a QED (electric) charge. That QCD charge is basically one color and one anticolor, minus the trace. So there are 8 different basis vectors that define the space for what the charge of a gluon is.

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Note that "charge", when used without a qualifier, typically refers to the electric charge (which is the origin of the term). Color charge and weak charge are named "charge" only by analogy - there is no physical mechanism underlying all quantities named "charge" (though there is a mathematical definition of why a physical property can be considered a charge or not).

Even mass itself can be viewed as a "charge" corresponding to the gravitational field.

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