您好,
''我和妈妈做了一个生日蛋糕.''
应该翻译成‘’I made a birthday cake with my mother .''
这句话可以这样来说
I and my mother have cooked a birthday cake together.
或者
I and mum have made a birthday cake together.
英语: My mother and I made a birthday cake.
我和妈妈做了一个生日蛋糕
I made a birthday cake with my mother