YOU SAID:

he wants me to go shopping with him to buy cake

INTO JAPANESE

彼は私にケーキを買うために彼と一緒に買い物に行きたいです

BACK INTO ENGLISH

He wants to go shopping with him to buy me a cake

INTO JAPANESE

彼は私と一緒に買い物に行きたいです

BACK INTO ENGLISH

He wants to go shopping with me

INTO JAPANESE

彼は私と一緒に買い物に行きたい

BACK INTO ENGLISH

He wants to go shopping with me