1
I would like going to Cambridge on holiday next summer.
I would like go to Cambridge on holiday next summer.
I would like to go to Cambridge on holiday next summer.
After would like, use to + verb: ‘I’d like to go home.’
Without would, like + -ing often means that you enjoy an activity: ‘I like going on holiday.’
See LIKE (1)
2
I’d like that he was more cautious.
I’d like him to be more cautious.
When you want another person to do or be something, use would like + person + to + verb: ‘I’d like him to be more cautious.’