Keep Coding

virtual void doSomething(std::function<void(std::error_code result)> callback) = 0
MockMethod1(doSomething, std::function<void(std::error_code result)> callback);
Now when I write EXPECT_CALL, how can I call "callback"
EXPECT_CALL(object, doSomething(testing::_)).WillRepeatedly( ??? );
What should I write at to call my callback?

No need to do custom action.
I found answer as different way,
here is what you need to do,
EXPECT_CALL(.....).WillRepeatedly(testing::InvokeArgument<1>(arg1, arg2, ..));

Use custom actions to achieve this. To achieve more flexibility, I suggest creating a template for an action, where template parameter signifies argument index of the callback function in doSomething. Here is how you do this:
ACTION_TEMPLATE(ExecuteCallback, HAS_1_TEMPLATE_PARAMS(unsigned, uIndex), AND_1_VALUE_PARAMS(callbackArg))
{
(std::get<uIndex>(args))(callbackArg);
}
Note that you can add more value parameters if needed. Now, in you test you call setup mock calls like this:
EXPECT_CALL(object, doSomething(testing::_)).WillRepeatedly(DoAll(ExecuteCallback<0>(err), Return()));