But in the pre-election economic and fiscal update (Prefu), released by Treasury last Wednesday, the total contribution over the next decade would be around $15b.
Goldsmith told Mike Hosking's Newstalk ZB show that the mistake didn't change its offering.
"It doesn't alter the fundamentals of our package which is the ability to offer tax cuts on the first of December - pay down debt faster than Labour - but it's an irritation."
National's fiscal plan was reviewed by independent economists NZIER. Goldsmith said its external reviewers had not picked it up either.
"I owned - we made the mistake. Our external reviewers missed it as well.
"The good news is it doesn't alter the fundamental numbers so we can still afford a tax cut and ultimately we can obsess about the error or we can focus on the thing that really matters to New Zealanders which is who has got the best economic plan to get us out of the hole we are in."
Hosking questioned whether the mistake struck to the heart of the party having credibility.
But Goldsmith played it down.
"We are talking about 15 years and a $600 billion budget by the end of it.
"What we are talking about is instead of getting our net debt down to 35 per cent in 2034 we will get it down to 36 per cent.
"That is in contrast to where Labour will have it which is 48 per cent. So there is still colossal differences between us and the government."
Goldsmith said Labour's approach was to put up taxes and add costs to businesses.
"[Labour are] doing all things that would be nice when the economy is booming but make it more difficult for people to take on jobs.
"Our contrast is we are going to cut taxes and we are going to make it easier for businesses to hire. That's what really matters."
Goldsmith claimed Labour would never willingly give the public back a cent of their money.
"They hate the thought of tax cuts. They always believe governments can spend your money better than you can. we have a different philosophy - we want to give it back. And ultimately NZers have that choice before them.
"Do they want to have it in their pocket or have Phil Twyford figuring out how to spend it on some boondoggle in the country."
National has promised tax cuts which they say will put $3000 in the back pocket of middle New Zealanders if they get elected.
Under National, the bottom tax threshold would be lifted from $14,000 to $20,000, the middle bracket would rise from $48,000 to $64,000 and the top tax threshold would be lifted from $70,000 to $90,000.
But these tax cuts are only temporary, coming into effect on December 1 this year and expiring on March 31, 2022.
Hosking questioned the temporary nature of the tax cuts.
Goldsmith said it was to stimulate the economy over what was set to be a difficult time for the next year or two.
"We are trying to stimulate what is going to be a difficult time for the next year or two. Just remember the economy shrunk by 12.2 per cent in the second quarter.
"These are extraordinary times we haven't had a temporary tax cut like this before in New Zealand's recent history. But we have to experiment, we have got to do things differently.
"And we think the best way to get the economy going is to put money back into New Zealanders pockets and let them make decisions about how they want to spend it."