An online fundraising account for the Sydney family had already raised A$132,000 (€88,000) in donations from strangers by Tuesday lunchtime after it was set up by friends to help the grieving family.
Seven-year-old Julian was killed by the van on Las Ramblas in the attack last Thursday while his mother, Jom, was knocked down and suffered multiple fractures in both legs.
The Go-fund me crowdfunding page, explains: "Andrew, Jom and Julian are a normal Aussie family whose lives have been devastated by the recent tragedy in Barcelona.
"Like all families they are paying a mortgage, bills and other sundries. As you can imagine there will be ongoing medical costs to get Jom back to full health.
"Many people have been asking how they may support the family at this time. We are asking for any contribution for those that may wish to help. This will assist with additional medical and funeral costs for the family. We thank you greatly for any support you may offer.”
The Julian & Jom Cadman Fund https://t.co/LaQGGZgMsm— tim roberts (@timmy_roberts1) August 21, 2017
Scott Bowman, a close friend and employer of Julian's father, who is a carpenter, started the crowdfunding on behalf of the devastated parents.
He told the Australia Daily Telegraph : "The concern we have got at the moment is their travel insurance might not cover acts of terrorism and Jom is going to have ongoing medical expenses.”
He said she may have to endure years of operations.
The heartbroken family paid tribute to the little boy, who was born in the UK and had both Australian and British nationality.
In a statement issued after his death was confirmed by Spanish authorities, the family said:
"Julian was a much loved and adored member of our family.
"As he was enjoying the sights of Barcelona with his mother, Julian was sadly taken from us.
"He was so energetic, funny and cheeky, always bringing a smile to our faces.
"We are so blessed to have had him in our lives and will remember his smiles and hold his memory dear to our hearts."
The family said it wanted to thank all those who helped searching for Julian.
"Your kindness was incredible during a difficult time," they added.
"We also acknowledge we are not the only family to be affected by the events, our prayers and thoughts are with all people affected.
"We will not be making any further comments on this tragedy and ask everyone, especially the media, to give us the privacy we need to grieve away from the public eye.”