I have set my $GOPATH, but it doesn't work

$ sudo go get -u github.com/golang/lint/golint
package github.com/golang/lint/golint: cannot download, $GOPATH not set. For more details see: go help gopath

I have set my $GOPATH:
(in ~/.bash_profile on my Mac)
export GOPATH=$HOME/gocode

And my go env:

$ go env
GOARCH="amd64"
GOBIN=""
GOCHAR="6"
GOEXE=""
GOHOSTARCH="amd64"
GOHOSTOS="darwin"
GOOS="darwin"
GOPATH="/Users/wildcat/gocode"
GORACE=""
GOROOT="/usr/local/go"
GOTOOLDIR="/usr/local/go/pkg/tool/darwin_amd64"
CC="gcc"
GOGCCFLAGS="-fPIC -m64 -pthread -fmessage-length=0 -fno-common"
CXX="g++"
CGO_ENABLED="1"

What's the problem?

The issue is that you are using sudo: it will use the root environment variable instead of the ones of your account.

You shouldn't need to use sudo, as I mentioned in "How to set GOPATH in Mac OS X 10.10":

• sudo has a default policy of resetting the Environment and setting a secure path
• unless you use the more complex sudo -E bash -c 'go get github.com/golang/lint/golint'):

For now, this should be enough:

go get -u github.com/golang/lint/golint

The OP adds a different go get command in the comments:

go install golang.org/x/tools/cmd/cover: 
  open /usr/local/go/pkg/tool/darwin_amd64/cover: permission denied 

That one would be using $GOTOOLDIR (set in your case to "/usr/local/go/pkg/tool/darwin_amd64")

As documented in "Permission denied error for 'go.tools'", running sudo -s then the go get command should work.

sudo according to man:
>sudo allows a permitted user to execute a command as the superuser or
another user, as specified by the security policy.

When using sudo you are executing as root. I would suggest that you remove sudo and try executing it.