Density error
I hate that erroneus way of referring to the relation between EAS, TAS and density! there is no such thing as density error.
If it was an error, pilots would wish for TAS indicator, instead of a normal ASI giving IAS. But we don't. We wouldn't mind to have an accurate EAS indicator, though. But we don't really need it, anyway.
Both IAS and EAS are "suffering" from that error, but we don't care. What we really want to know is what is the dynamic pressure around us. EAS would give exactly that. TAS would not.
IAS is subject to position, instrument and compressibility error.
The question makes no sense. Climbing at constant EAS? EAS will be the same, of course! (that's why it is constant)