The \$I^2R\$ loss in transformer is eddy current loss or copper loss?
'Copper loss' is I2R power loss in the windings due to current flowing through them. As this current increases with higher loading, so copper loss also increases as loading increases. 

Eddy current loss is power loss in the magnetic core due to current induced into it (each lamination in the core is effectively a shorted turn, but the silicon steel has relatively high resistance which keeps the current down). The induced voltage - and thus current and power loss - doesn't change with loading because the magnetic flux in the core doesn't change. This is also I2R loss, but it is not copper loss. 

To summarize, there are two places in the transformer where I2R losses occur - in the magnetic core and in the windings. However, only the windings have a power loss proportional to load current. That loss can rightly be called 'copper loss' because only the windings are made of copper.