Which part of the federal government is not mentioned in the constitution but by customs has affected the impact of the constitution

I agree with the person above - the answer should be the Cabinet.

The Cabinet, in the American government, refers to a body which is there to advise the President. Although it is their purpose to provide the President with their insights, ultimately, the President can choose not to listen to the Cabinet's members. It is a body which is not explicitly mentioned in the Constitution, however it plays an important part in the government.

The Cabinet

I'm sure that's the answer