db={"a":[{"academic_year":"2021-2022",_id:ObjectId("6345659fd06188306de0deae")}],"b":[{b1:1,b2:2,b3:[{b3_1:5,b3_2:4,b3_3:4},{b3_1:1,b3_2:4,b3_3:2},{b3_1:5,b3_2:1,b3_3:2}],b4:ObjectId("6345659fd06188306de0deae")}]}

db.b.aggregate([{"$addFields":{"b3":{"$map":{"input":"$b3","as":"b","in":{"$mergeObjects":["$$b",{total:{$sum:["$$b.b3_1","$$b.b3_2","$$b.b3_3"]}}]}}}}},{$addFields:{BigTotal:{$sum:["$b1","$b2",{"$reduce":{"input":"$b3","initialValue":0,"in":{$sum:["$$value","$$this.total"]}}}]}}},{"$lookup":{"from":"a","localField":"b4","foreignField":"_id","as":"aLookup"}},{"$unwind":"$aLookup"},/** data wrangling/cosmetics*/{"$replaceRoot":{"newRoot":{"$mergeObjects":["$$ROOT","$aLookup"]}}},{"$unset":["aLookup","b4"]}])