Hi Helen, Both sentences mean pretty much same. 어제는 철수 씨 생일이었는 줄 몰랐어요. = I didn't know it was 철수's birthday yesterday. 어제가 철수 씨 생일이었는 줄 몰랐어요. = I didn't know that yesterday was 철수's birthday. Hope it helps.

어제는 철수 씨 생일이었는 줄 몰랐어요 The basic structure is 어제는 몰랐어요 Yesterday, I didn't know The whole sentence means Yesterday, I didn't know that a certain day was Cheolsu's birthday. 어제가 철수 씨 생일이었는 줄 몰랐어요 The basic structure is (저는) 몰랐어요 I din't know The whole sentence means I didn't know that yesterday was Cheolsu's birthday.