In this post we saw how these 3 'reporting verbs' are followed by 'verb + ing'.
Today we'll compare this with 'told' (Past Tense of 'tell').
Direct Speech: "I've eaten your cake."
Reported Speech: "He told me that he had eaten my cake".
There are 2 past actions in this sentence.
1. He ate the cake.
2. He told me.
So you need Past Perfect to show which action came first:
'He ate the cake and then he told me about it' just sounds weird.
You can replace 'told me' with a more precise word like 'confessed' or 'admitted' but this means that the Past Perfect 'had' changes to 'having' because these verbs are followed by 'ing'.
In fast speech, people don't stick to the 'rules' of Reported Speech.
A person would probably say:
"He said he ate my cake".
So don't worry too much about this rule!
Notice that 'deny' follows the same pattern and is more likely to replace 'having stolen' with 'stealing':
He denied stealing my cake.